Regardless of the surface, there will be falls and bumps as she learns to crawl (and, later, walk). Keeping her at floor level is a good plan, though.
There are two things I'd suggest looking for: reasonable traction and moderate padding.
The traction is more important for learning how crawling works than for potential slips causing injuries. If her legs and knees keep sliding out from under her, she'll never figure out crawling because she can't even get herself up on all fours. (A hardwood or tile floor is only going to be slippery if she's wearing pants/tights, which would prevent her from getting good traction with her knees and legs. However, her hands are what is really providing support for her upper body and head; those are unlikely to slip much on a hard surface, so there is little head-bump risk.)
The padding prevents her from having very hard bumps on the head (although I would not worry much about bumps -- it's not from a great height). Carpet provides good traction and also a moderately padded surface. If you live somewhere with only hard flooring, a blanket spread on the floor can provide padding.
Ironically, I think my daughter ended up falling face-first more often on a particular carpet in her grandma's house because it had a lot of static cling with her pants, which threw off her movement :)