The wife would not allow it. Now she is two she might, but the wife is not really the camper type. Bugs tend to freak her out and Florida is full of them.
I don't think it's that bad of an idea. As long as you're in a clean, safe campground and keep an eye on them, I don't see why everyone can't have a good time.
I don't think I would take an infant out camping. The weather is a little too unpredictable this time of year and I wouldn't want to get caught out in chilly damp weather with a baby.