Discouraging tummy sleeping???

I’ve noticed my daughter ( 1 month) really likes to sleep on her tummy.. I always put her to sleep in her back and she starts stirring in a couple minutes and eventually wakes herself up! While she is nursing she falls asleep fine and will stay asleep for hours! And sometimes I’ll take her off of me and place her on her belly on my bed (while I am awake and keeping an eye) and she will sleep there fine to!!

I’m thinking either I just have to move her as soon as she falls asleep to her back?

Or get make one of those rice pillow things and put it on her.. but I’m terrified of doing that because she shouldn’t sleep with anything... I just don’t know..