Brooke,
Thanks for your question.
You will definitely want to check with the folks at Mears about how to do this. Their site for the new Mears Connect service does require you to have a flight schedule for both pickup and return times. However if you contact them via their site, or choose one of their other services, you should be able to use them for your transportation needs. Also note that while they track flights for incoming guests, they do so to know if you are going to be late due to flight delays. You might have a way to set a time with a different incoming flight that morning, even if you are not on that actual plane.
I did stay in that Orlando airport hotel once, and it was so exciting to be right there in the hustle and bustle of people coming and going. There is an electricity to the airport as you watch families arriving for their magical adventures. I strongly recommend that you enjoy dinner, or at least a snack from the lobby of the hotel above the airport atrium that the hotel surrounds. It is just a fun people-watching experience. Also, if the weather cooperates, you should plan some pool time. Their pool is on the roof, and has great views of the workings of the airport. It is definitely a unique view to take in.
A final suggestion is this: consider changing that first night stay from the airport to
Disney's Caribbean Beach Resort. If cost is a concern, you could also consider staying at the nearby
Disney's Pop Century Resort. You may find that the latter is comparable in pricing to your airport stay, and you will get even more out of your first day. Heck, you will just be a skyliner ride away from two parks, and you won't have that rush hour drive from the airport to Walt Disney World! Disney will even transfer your bags from Pop Century to the Caribbean Beach for you, so that you don't waste any time during those prime park-visiting hours.
Write me back if you have any further questions!
Have a Magical Vacation!
Doug