My DS is 7 months now, but from about 4 weeks old, he started to roll/wiggle over on his own onto his belly. There was NOTHING I could do to make him stay on his back or side, plus he hated every minute of sleeping on his back and woke up all the time. So, from 4 weeks on---he was a tummy sleeper ONLY. I just made sure to NOT put anything in his crib to ensure he wouldn't have anyting in the way of his little face that could possibly obstruct his breathing.

My pediatrician is old school----and she totally supports and encourages tummy sleeping as babies sleep better and longer that way. The risk of SIDS is very rare---babies die more often of aspiration and choking on formula and saliva. If your DD can at least turn/switch her head position from one side to the other, then she will be OK.
Don't get me wrong, the first couple of weeks of tummy sleeping, I would wake up a couple of times a night to make sure everything was OK with DS---just to make sure. Ya know---mama nerves! hehe

Also note, from 4 weeks on, he became a MUCh better sleeper. He started sleeping through the night first 6-8 hours minimum and now sleeps minimum of 10 hours.