I don't know about NEVER bringing your kids to Burningman-you just have to go with the right expectations and BE REALLY PREPARED! You also need to really take care of yourself out there or you will be useless as a caretaker!
www.burningman.com/preparat...t_bm.html

IMHO, it is probably as dangerous to drive your kid down for a day at Disneyland (substitute local theme park as needed) as to take them to a day at Burningman (properly prepared). For one thing, the drive through LA (usually several hours of crawling traffic) is heavy with pollution, deisel emissions, smog, carbon monoxide-probably at least as dangerous to babies and young children as playadust. Then you get to Disneyland, which is usually about 100-110 or more degrees in the summer, given that it is one big giant blacktop lot soaking up all the rays of the sun. Add to that the huge, dense crowds that your children could easily get lost in, the "Disturbing" characters that scare and grab your children for photos (my daughter has been especially freaked out by an overly friendly "Captain Hook"; "Cruella DeVille" who joked around -in character -about how she wanted to make a coat out of dalmation puppies, and even by Mickey Mouse-what kid naturally is drawn to giant rodents the first time he or she sees them!?) Then there is the fried food and softdrinks and sugar that they are offering as "lunch" or "snacks" (I have personally never seen a healthy kid's meal at Disneyland-we bring our own). Add to that the rides that spin your kids around till they feel like they might lose their cotton candy, and the Pirate's of the Carribbean Ride that will give your kids nightmares for the next 6 months (no joke-my friend's little daughter is still freaked out)..... I have seen WAY more crying kids at Disneyland than I ever did in Kidsville at Burningman (mine included) so maybe you are equally negligent for taking your child to Disneyland as you are for taking them to Burningman. Personally, I think Burningman by day, away from "The Temple of Atonement" or "Trippin' All Day" Camp is probably the lesser of 2 evils!

I brought my 3 year old daughter last year-I am not a big fan of sheltering her from the "real world" or leaving her for more than 4 or 5 hours (much less a week) with someone else yet(all into this Attachment Parenting Philosopy I guess). Here is a blog from our experience, which I've trotted out a couple of times so plenty of people have already seen it.

people.tribe.net/tigerlily/blog

Quick Summary: It was a lot of fun. My 3 year old and my friend's little boy LOVED it! They were not phased by anything and were healthy and happy all week (but the weather conditions were pretty mellow last year). For me-not as fun as past years-it is more work actually being responsible for someone else other than yourself. However, it was WAY more fun than skipping it and missing out on the experience and just staying home in the default world of traffic and everyday pollutants. I think if I hadn't had past AMAZINGLY PERFECT Burns to compare it to, I wouldn't say it was less fun. Just Different.

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It "takes a village" to bring your child to Burningman-here are some groups that bring their kids to Burningman (or at least are Burners at heart, and raising their kids with the Principles of Burningman)

Southern California Burner Families:
tribes.tribe.net/socalburnerfamilies

Burning Moms (There is a ton of postings every day on a Yahoo Group you can ask to join-but I'm not in charge of that one)
burningmoms.tribe.net/

Kidsville (The experts-some have been bringing their kids for 10+ years) There is more discussion on a Yahoo Group you can ask to join:
tribes.tribe.net/kidsville

Burning Families:
burningfamilies.tribe.net/

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Finally, you know how"Heloise of the Playa" tells you to take care of YOURSELF when you pack? Well, here are some "must haves" from my perspective for bringing young kids:

A Bike Trailer, so you can actually go out and see things. Try to pick one that puts a shade over your child's head while you are riding (or make a shade) and also one with a plastic cover so your bike isn't kicking playa dust in his or her face the whole time! Best to get one with the converter kit so you can turn it into a stroller to taking sleeping baby into domes or Center Camp (I found mine on Craig's List last year for $30. It was pretty faded, so this year we painted it orange and put tiger stripes on it to match my furry bike).

A Misty Mate (so you can mist the little one every 15 minutes or so-or just keep it constantly on in the bike trailer if it's hot-that will keep them - and you cooler than just about anything else).

A Camelback attached to the bike trailer so that while your child is riding around he or she can get a drink at any time

A kiddie pool or a large bowl (I found one at the 99 cents store last year big enough to give 3 year olds a bath in! Not too much water wasted and a nice cool down)

Gatorade, Salty snacks or Pedialyte Popcicles-Hot kids, just like adults, lose electrolytes when they sweat so they need to be replenished. I went further than just suggesting (overly sugary) Gatorade, though, because if your kid is like mine, you are not going to talk 'em into drinking it-while she hates the stuff, my friend's little boy guzzled it down.

A Playpen or a Baby Yard to put your child in for those moments when you can't give them your full attention. You don't want them wandering off and getting lost or stepping in front of a bicycle or art car while you are putting up your shade structure or digging through your cooler looking for the pedialyte pops.

Baby Goggles-they sell them on the internet. Baby sunglasses and a hat as well-if you're like us, you probably already have 20 of them!

Those "painter's respiratory masks" for when the dust kicks up. If you put a pom pom nose on it and maybe a doggy, bear or (in my case) leopard's mouth on it, you can probably convince your child to wear it when the dust kicks up. I wish I had a picture, but last year it was only really dusty once, when we were indoors. The kids wore the masks once or twice and other than that we just carried them everywhere "just in case".

Headphone Ear Protection-if you are going to take your child anywhere loud. I got them a while ago for my daughter, who thinks the coffee grinder is "Too Loud!" We didn't really go "clubbing" at Burningman last year-hung out at Kidsville (and sometimes Center Camp) for more quiet pursuits at night. I had them on her for Mutaytor at "Lightning in a Bottle" though, and they worked fine (as in she didn't try to take them off, little rebel that she usually is!)

I don't know if your 18 month old is potty trained, but if so, my friend had an empty wide mouthed plastic bottle for her little boy to use as a urinal, and I had a widemouthed plastic Folger's Jar for my little one to use as a bathroom. If you are potty training, you know how hard it is for them to "wait their turn" near a public (possibly yucky and always too big for them) bathroom!

Finally-3 strong suggestions:

A Trailer or RV or VW Bus or something Solid and insulated with a bathroom and sink. We did not have air conditioning, but that might be nice for naptime too! I am not a big fan of kids in tents. Not only do they get too hot when the sun comes up, but last year we sat in my trailer while the Wednesday windstorm flattened my neighbor's tent (no one was home). I don't think it was ever the same. I wouldn't want to live in it after the polesbroke and it filled with dust-she didn't either and moved in with friends! Also, the bathroom in my Camper was a lifesaver at 10pm or 1am or 4 in the morning when I had to go-I didn't have to leave a sleeping child to walk off to the bathroom, and when she had to go, I didn't have to drag her into a yucky portapotty while I went or she had to go (only downside I can see from that is that we were not exposed to the idea of fingerpainting in poo which has been so eloquently described by many Tribe members who saw it first hand last year-that's OK though!).

An Art Car, or something you can hang out in on Burn Night, when the crowds are really big- so your kid can actually see.

Friends with kids, and/or the other parent to help share/take turns entertaining the kid(s) so you can have a little break now and then.
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Here are some pictures from 2006:
Girl and Man
tribes.tribe.net/socalburn...23f57a12de

Conversing over a"Big Ball of Pooh" at Center Camp
tribes.tribe.net/socalburn...fcb165eee2

Some Burningman "Rides"
tribes.tribe.net/socalburn...1349b364a5
tribes.tribe.net/socalburn...5a9951be2a
tribes.tribe.net/socalburn...44c3138e4c