WDW doesn't put any restrictions on people riding with a cast, but you might want to think about the thrill rides. For example, would she need her arm to hold on or will her arm be swinging around during the ride? Also, for some things, like TOT, her arms will be dead weight going up and coming down. Whether or not she can do thrill rides is probably a question for her doctor.
As for a wheelchair, they do have small, limited numbers of child size wheelchairs (first come, first served), but most of the ones for rent in the parks are adult size. For an average 8 year old, that means the arm rests come anywhere between mid-chest and shoulder height. Also, the seat depth being adult sized means the seat edge hits a child below the knee, so they either have to sit forward in the seat so their knees can bend or they have to sit back in the seat and have their legs sticking straight out. You can rent pediatric wheelchairs and special needs strollers (basically large umbrella strollers that will hold someone up to 100 pounds) from these places:
Care Medical:
http://www.caremedicalequipment.com/
Phone (407) 856-2273 Toll Free U.S and Canada (800) 741-2282
http://www.all-about-kids.com/main.htm
A better option might be just to rent a WDW stroller. They come in different sizes and (at least per some WDW CMs who post on the boards) the largest size will fit up to a small 12 year old.
Most of the lines at WDW are wheelchair accessible, so wheelchair users wait in the same line as everyone else (you don't need anything to be able to bring a wheelchair in line). I probably would just park the stroller or wheelchair and have her walk in most lines because it will be easier. If you use fastpass as much as possible and get to the parks early, your waits in line will be decreased.
If she needs to lie down and take a rest, there is a First Aid station in each park. They have cots in individual cubicles and it's dim, cool and quiet. The CMs are super-nice. Be sure to bring her sling along each day and also pain medication, in case she needs it.