Babies are precious but they are also a burden. They are a huge financial and emotional burden.
The best situation to bring a precious baby into is one where you are in a stable, equal relationship with another adult who is willing to contribute half the effort required to take care of them. If you're the one going through pregnancy and childbirth and postpartum, potentially breastfeeding, having to take at least a short time off work, your partner needs to be contributing more than half the effort in other ways, e.g. earning, housework, nappies etc.
The next best situation to bring a precious baby into is one where your partner isn't quite contributing enough but still, all things considered, makes your life easier and more pleasant than if they weren't in it.
The next best situation after that to bring a precious baby into is one where you are completely on your own and you know that, but you can do things your own way and you aren't having to support another adult.
The worst situation to bring a precious baby into is one where you are in a relationship with another adult who makes your life harder, not easier.
The OP certainly isn't in the first situation, so she needs to take a good hard look at this relationship and decide whether she's in the second best situation or the worst situation. If her partner is making things harder rather than easier she should bin him off and go it alone.
And yes, she may well not want to leave her baby at three months old, but she might not have the choice. Her partner isn't stepping up, and someone needs to pay the bills.