Former college athletic trainer here: bruising is actually a good sign. Yes, it is normal to see brusing so quickly. A sprain is a stretching or tearing of soft tissue, so when that happens, there is blood, thus the bruising and swelling. The best thing to do is to follow the RICE program, rest, ice, compression, elevation (be careful with the compression as if it is still swelling, it will soon get too tight). I wouldn't use anything but ice for at least 48 hours, heat will increase swelling. After 48 hours, if needed, you can alternate ice and heat, just start and end with heat (ice for 10 minutes, heat for 10 minutes, ice for 10 minutes then nothing for at least an hour). For the athletes we did this all day long, with an 8 year old, yeah right! Kids heal pretty fast.
As for it being broken, yes, it is possible, but usually you don't have swelling and bruising right away with a break, the bone gives before the ligaments give so you don't really stretch them as much with a break, usually. With a break, usually the next day have have a very distinct line of bruising, almost like someone drew the bruise on your skin. You will get a similar line of bruising with a sprain, but usually not for a few days and that will be mixed in with all the other bruising.
You can still have broken bones in your leg, ankle and foot and still be able to walk on them pain free, it just depends on what kind of fracture you have and where it is in your foot ankle or leg. We had a boy on our cross country team run the entire season with a broken bone in his foot (the team taking first in state and 7th in Nationals even).
Chances are it is just a sprain. It will be very sore in the morning after sleeping all night and it getting stiff. Have her try to walk as normally as possible. The motion of walking will also help get the blood moving in the area (to a point-I wouldn't suggest walking Disney on a fresh sprain).