As the others have said, tummy time doesn't have to be on the floor. Lay her on you, across your lap or hold her face down across your arm.

I also second the rolled up towel, it made a big difference to DS's enjoyment of tummy time. I wouldn't worry about her not learning to lift her head up, she'll do it. I'm going through this at the moment as DS has great head control (checked by paed today) but he's not pushing himself up...he's had heaps of tummy time...so it's just a wait for him to get stronger.