First, welcome to the Forum! I am very glad you came here before spending money! Lots of very good information above!
I suggest you spend a few months reading everything you can find on forums like this. Look at the articles in our Library as well. As you do, many questions will be answered and many more important questions raised.
As Rene said, used is very highly suggested. Avoid the ones which were abused or had pets, etc. I understand allergies and associated issues. New campers may well have materials that need to outgas for a year or two before they are suitable for you. Let the first owner get the factory problems fixed. Save some money. Reduce the financial pain if or when you trade or sell it.
I just bought a 8 year old gently used, well maintained FW for 38% of the original sale price. It takes some time, but they are out there in the floor plan you want.
The truck may be an issue. As you research, you will see lots of threads on weights and capacities. F250, depending on the year and exact configuration, will have around 2500 lbs Payload or carrying capacity. This may sound like a lot of weight, but it must include the FW pin wt (20% of actual loaded weight), the FW hitch (around 200#), the weight of all passengers, car seats, snacks, games and anything else carried in the truck. A 12,000# FW means 2400# pin wt + 200# hitch, and your payload is gone before the DRIVER gets into the truck.
If you find a bumper pull TT bunk house, then this calculation is 10 - 12% of actual loaded weight, or 1450# for a 12,000# TT, plus 80# hitch, leaving 1000# for passengers and cargo.
Look at lots of styles and brands, new and used to get an idea of what is available and what you PERSONALLY like and dislike.
HAPPY HUNTING!