I don't think you're crazy at all! (but I take my kids everywhere...just got back from Europe...2 wks through Turkey, Greece and Italy with a 5 yo and 13 mo, thats crazy! lol)
Its not going to be camping by yourselves. You'll be more tired. You probably won't be able to take everything in. But in exchange you'll have wonderful memories with little one-and you'll be getting baby used to this type of travel from a young age.
One thing I'd consider is how is the baby sleeping at night these days? If waking frequently still, you may not want to have a baby (like mine) thats waking up 2-3 times a night, or very early, crying loudly, while in a tent around other tenters.
Other than the sleeping situation I don't see any difference in tenting it, or staying in an rv, cabin, or hotel with a baby! You and the baby will have a blast. There is so much to do in FW. Carriage rides, baby will love the horses and animals. Fireworks from the beach. And a wonderful pool just his/her size

As far as bug spray, I would never put deet of any strength on a baby. I think the new 'natural' baby sprays are just as good. California Baby (target or online) makes a natural citronella type spray. We go to FL 4-5 times a year and I've always put that on the kids and it works. There's also mosq repelling stickers now, and wristbands.