Definitely don't put it in with a female quail unless she's broody, even if they are broody they're not good mums! Can't it go back in with its own mum? Otherwise someone with a broody pekin could take it?
We had a (very broody) quail with chicks this year, nothing like a broody chicken
And unfortunately I had been warned about their lack of mothering skills but went ahead with it anyway, silly me
Good luck, hope yours does alright