Can I pour a new concrete shower base over the existing concrete floor?

Depends how thick you are going to pour it. Min should be about 2 1/2 inches thick with High strength concrete and a wire mesh 6 x 6 square 10 gage double laid offset to each other.
If you make it 3" thick a single matt layer of wire in fine . The best over all thickness is 3 1/2 inches and still use wire in it