The writers state that Supergirl will have different powers that Superman doesn't have, as the yellow sun may effect female Kryptonians differently.
Great first issue, btw!
IGN: Is Supergirl's power set the exact same as Superman, or will she differ in some way?
Green & Johnson: The basics are similar: flight, strength, heat vision, etc. But the power levels are different, and there is a very specific reason why that will be revealed in the course of the story. And who's to say that the yellow sun affects Kryptonian males and females the same way? We will be revealing new abilities that her cousin doesn't have.