Dd slept on her tummy from the day she came home. Ds1 started on his back, in textbook style, but was on his tummy within weeks. Ds2 varies between side and tummy. Some babies just do not sleep well on their backs.
Make sure her room is well-ventilated, that she isn't over-wrapped (touch her skin between her shoulderblades to guage how warm she is), that she sleeps in pure cotton, that nobody smokes around her, and that nobody has smokey clothes around her, and she should be fine. Best of all, co-sleep with her if your are breasfteeding.
Also tip her cot up or put a small wedge under her so that her head is higher than her feet.