Is it ok for a one month old to sleep on her tummy for naps?

I'm a FTM and my DD is one month old tomorrow but for the last few weeks has not been napping well at all...Mayb 10 minutes 15 tops, this makes for a very very cranky and fussy little girl who is extremely over tired and still refuses to go to bed sometimes until 1am.. I'm wondering if it's OK to let her sleep on her tummy just for naps..I've tried once and she was wonderful..She constantly fusses when she sleeps on her back for bed but I'm wayyy to nervous to have her sleep on her tummy for bed so she'll just have to be fussy at night for now..if I can get her to nap well on her tummy that's better than her being sleepless all day AND night so a nap for max of 3 hours should be OK right? She is a good healthy baby... Breastfeeding like a champ and can already turn her head when doing tummy time.. just looking for advice no judgement please..