Any DSLR, with the right lens and right photographer, will be able to shoot action with little trouble. No worries there.
The keys would be a more sensitive lens of course, something F2.8 or better would be best, higher ISO as needed, to enure shutter speeds of 1/250 or better. A fast continuous shooting mode might be useful too, though you can get by without those if you have good timing. It requires a wee bit of skill and practice, but the DSLRs will give you the latitude to learn.
Shooting slightly wider, and cropping in does help with action - both in allowing you to ensure you get the subjects fully in the frame, and to allow you to nicely compose the shots by cropping for best effect. You don't want to crop a lot, or you lose resolution for printing, but most DSLRs have enough room to trim 20-30% of the original, and still print large.
Don't overlook any brand - feel, handling, and features play a part of your decision - you should be comfortable shooting with and holding the camera. Sony has larger, stable cameras with built in stabilization in the body, and their newest bunch have some of the better high ISO performance available. Pentax make small and light DSLRs with solid ergonomics and also have in-body stabilization. Olympus makes both small DSLRs as well as a new class of cameras that use the same sensors, but drop the mirror systems, so they perform as well as their DSLRs in low light, speed, and image quality, but are half the size of DSLRs - a tue hybrid between P&S and DSLR. So while Canon and Nikon are both excellent, there's a lot of feature content and creativity going on with the other three major brands too...and they're all worth a look and feel.