How does your baby sleep

My LO sleeps on her back for an hour or so, but does not like it at all. I will put her on her tummy while I'm in the same room and she sleeps so much better!! Up to 2-4hrs and wakes up much happier. She will be a month old Saturday. I want to let her sleep on her belly in the pack n play or crib, but the whole sids thing has me scared to. Suggestions? Just let her? Bad idea?