I agree with the others that you don't want to rely on one from the parks. Besides not being the most comfortable and not having a way to elevate her leg, if you rent from the parks, you won't have one for use in the resort. I don't know what resort you are staying at, but the resorts are very large and having a wheelchair there would make your trip much more pleasant.
Also, if you don't have a wheelchair with you, the walk from where the bus or monorail lets you off might be enough to tire her out for the whole day. The monorail stations are at 2nd floor level, which is not a problem when you get on at a resort, but is a long walk up a steep ramp at MK and the TTC.
The disABILITIES FAQs thread has information about where to rent (with links), and about riding buses, boats and monorails.
You are correct that transporting the wheelchair by plane is not a problem. The airlines are required to carry the wheelchair at no extra charge. You can gate check the wheelchair - ask before they start the boarding process because they will need to give you a special gate check tag for it. That way, you can bring the wheelchair right to the gate and it will be delivered to the gate in Orlando. Before you leave the wheelchair, make sure it is folded. Remove anything that is removable and if you have anything that is unfolded folded or moved out (like legrests being elevated) bring them back in as close as possible. Doing that will help prevent damage.
If you would rather not bring the wheelchair with you, you can get skycap wheelchair service from the airline and rent a wheelchair from one of the off-site places to be delivered to your resort.
Good luck on your trip.