Sure there are dangers when camping, but there are equally as many in your house (maybe more). DON'T LET THIS STOP YOU FROM GOING! You just need to be prepared. I have a four year old that we have car camped with since she was 4 months old and backpacked with her at 5 months. It went so well, we felt completely comfortable doing it all again with our daughter (now 4 years old) and her brother (4 months old). Car camping is the easiest. In the worst case, you just hop in your car and you're back home - no big deal. If you are camping pretty far from home, maybe you want to try a "practice" night in your backyard. We don't have a backyard, so we went camping at Mt Laguna, which is less than an hour from our house.
Here are the things that I found to be helpful. Number one, be flexible. Things happen. Relax. You're there to have fun, not get stressed about every little speck of dirt or bump that happens.
Second, my husband and I have done a lot of camping. While this is not necessary, it helps to be comfortable with cooking, cleaning, etc in camp versus home. If you haven't done too much camping, talk to friends that have about their experiences.
Third, bring a pack and play. This was my absolute favorite thing for camping. The baby is contained and not racing off into the water. I used this until our daughter was almost 2 years old.
As for sleeping arrangements, my husband and I have sleeping bags that zip together (if you ask at REI or another outdoor store, several brands - ours is Marmot - make bags with a zipper on either side). This allowed us to put the baby between us. The baby slept with a fleece sleeper and a beanie hat. Both my children did just fine and sometimes were even too hot with this set-up. Be sure to have a Thermarest for each adult, too, as this insulates you from the ground. Some friends of ours tried this, too, but they had difficulty sleeping because they were worried they would role over onto the baby. They adapted by bringing the car seat into the tent and doing a little heavier fleece and a blanket.
As for a tent, I seem to be in the minority here, but I don't think you need a tent as big as a house. We fit our family of 4 into a three person tent just fine. Get some nice camp chairs. You're camping to be outside, not inside the tent.
Good camp chairs with arms work great for breastfeeding.
Bring more wipes than you think you could possible use. They're great for a quick bath for baby and for Mom. Also, make sure to have Purell or some other alcohol hand sanitizer.
We found a onezie fleece coat very helpful, too. We also had a raincoat onezie from LandsEnd. I went looking for another one for my four month old and they don't make them any more, but try looking around for one. In addition to keeping baby dry in the rain, it acts as a wind guard. But best of all if the baby is out crawling, it keeps them a little cleaner than a jacket and pants.
Also, remember, the more stuff you bring, the more you have to fit in your car and then clean when you get home.
Put together a first aid kit with Tylonol and Benedryl. Also, make sure you have sunscreen. Tlk to the doctor, but mine said it was okay for once our daughter was 6 months old.
Lastly, have fun!
I hope this helpful. All of us have really loved our camping experiences. I also went lightweightbackpacker.com when I was preparing for our first trip. Some of the information won't help, but it's worth a little investigation.