Bless you both. Things seem to've happened very quickly. It actually might be a good thing that you've got this separation at the moment, which'll give you a breathing space, and time to reflect on what's been going wrong, and how you might put them right.
Prozac is alright on a temporary basis, but can kill libido. I don't think your partner needs counselling so much, as friends and family to talk to, and who'll support her. It's not easy with a young baby, & the poor woman probably can't see an end to things, what with being short of money, and being apart. I do hope you get that job. If not - take another, even if it's not what you really want. Try and help with looking after the baby when you visit, & let your partner have a rest. You don't need to go out & spend a lot. Your money'd be better being saved, and some going towards the baby's upkeep. x