is it bad that my babygirl sleeps better on her tummy?? (long)

Jean
My babygirl is a month old and she has recently begun to have a hard time sleeping. She will not sleep on her back or even her side for longer than 30-40 mins a time all day. She gets extremely fussy at night and just will not settle down. However when I have put her on her tummy for naps (totally supervised) she sleeps so peacefully. 
 this evening I placed her on her tummy at 8pm and my husband and I prepped for work and had a chance to shower together, spend some alone time, and even just sit and talk and laugh while babygirl slept in her crib in the same room on her tummy for TWO and a half hours uninterrupted!!! I checked on her from time to time to assure she's breathing and has a clear airway nothing blocking her mouth.
 She has now been sleep almost three hours and I'm debating if I will leave her on her tummy. This is so rare that she stays sleep for longer than 45mins. I know the risks of SIDS but I also know that they are just risks and many have let their children sleep on their tummy for long time with no problem. Am i wrong for wanting to let her stay asleep on her tummy???? She has even moved and turned her heard and adjusted her body a few times. 
No rude comments plse but constructive and helpful thoughts are welcome.