4 month old belly sleeping?

My daughter is now 4 moths old, and just recently I discovered that she sleeps much better on her belly. I was wondering if it was safe? I've heard the spew about SIDS, babies that die on their bellies is due to suffocation, SIDS in completely unexplained, so I have the blanket no wear near her face, she hasn't gotten down the coordination yet to roll over, however she can push herself up with her arms about 90 degrees and turns her head very easily while on her stomach. Her muscles are at a 5 month development level, she has great control over her head and back. I was put on my belly as a baby and so were many others I know, I heard that if a baby can roll over OR push themselves up it's safe. Is there any reason I shouldn't?