We also camped with our daughter, although we borrowed my sister's pop up trailer for the first few years. We put cushions on the floor and blocked her in. You can rent them for a weekend, I think. She was born in September, so we went several times the next summer. She did get sick on one of our trips (at 11 mos.), but we were at my aunt and uncle's pig roast, so there were some foods that sat out a while. Plus, other than an upset stomach, she seemed alright. The traffic of the nearby highway combined with the fresh air helped her sleep better.
She wasn't all that mobile, so containing her wasn't much of a problem. We let her roll around on a blanket and pushed her on the swings at the playground. However, we did have to keep her in the shade for several hours because both her and I have extremely fair skin. We also brought the bug spray and benedryl, just in case. Wet wipes and hand sanitizer come with us every trip, and she had a bath when we got home. We used formula mix, so it wasn't a big deal.
The one thing you will want to consider is how strict you are with routine. Because both of us worked a lot at the time, she didn't have much of a routine (I don't recommend this), so it was not a big deal. However, if you go camping with friends (we have more fun that way), one of you may have to miss part of the evening to get her to sleep. Plus, it could disrupt the routine that you have set up at home a little. You also may want to consider where you go. Ours was a loud cryer and did not sleep well, so we tried to get secluded sites (backyards, less crowded weekends, etc.). Most campgrounds are family friendly, but it can get frustrating when your baby won't stop crying and your kid doesn't do what they're told.
Have fun! I don't know if we'll go this year because our second baby is coming next month. But knowing my husband, he'll push for it anyway. One of the mothers that we camp with loves babies, so I'll probably get her to go and we'll play pass the baby.