We park at DFW all the time and fly. There are several options. We prefer the covered parking right at the terminal and we use those spots. I don't remember but I think we pay around $16 a day. My husband is flying in and out of DFW and Love field weekly and we use the closest parking which is more expensive.
NOW, that said, there are some cheaper options on parking. The Parking Spot is not on the DFW premises but you park there (reasonalbly priced) and they shuttle you to the terminal. Park and Fly is very similar.
If you prefer no to have any shuttle....park on the outlying lots at DFW which are cheaper. You just park there and then catch the DFW shuttle to the terminal.
You can check the DFW parking options on their website as well. We've parked our car there for a week and it was all good but we paid $100 or so to do it. We especially like the limo service (Allen limo) because they pick us up at our home, take us directly to the correct terminal, then on the way home, they are right outside waiting on us.
This is especially helpful for a ride home because you are usually tired from travel, etc. We landed one morning at 5am from Hawaii and the last thing we wanted to do was get in DFW traffic. The limo is great for that service and not overly expensive.
Enjoy your trip!!! It will all work out and you will have a magical time!! We've done Disney about 7 times. We don't use the Disney shuttles either...we prefer private taxi.