Actually, I don't have a real one, but I saw them on Google.In practise, not much. Do you have a real context?
doll's pram is what I would write, it is a pram for a doll. By definition it would be small and could equally well be called a toy-pram.
toy-pram indicates it is a pram for playing with
doll pram seems wrong to me, but I wouldn't be surprised to hear someone use it.