If she doesn't vomit much, it sounds more like she has silent reflux. Or she could very well be swallowing any vomits while in bed. DD2 does a bit of both when she's in bed but she certainly spews all day

Anyway, the point I was trying to make is if she copes ok in bed, she'll be fine on her back Tummy time will probably be tough so just give her quick goes well after a feed.

DD2 wasn't very good at tummy time until about 4 weeks ago (she's 20 weeks now) as it was difficult to get her on her belly due to her reflux. She was so bad the health care nurse said she was like a 6 week old at her 4 month checkup! She spoke to me about the possibility of low muscle tone but all was good within a week or so of that appointment. So keep trying hon and don't stress