Couples threaten to break up all the time. So you need to work out if this is a heavy row, or a full-on end-of-the-world apocalypse scenario.
Saving a relationship is not the easy option, and it's often harder than splitting up. It involves both sides swallowing their pride, and trying to solve some of the deeper problems in the relationship, rather than the surface problems that seem more immediate. Also, while it may feel that splitting up will be a magic bullet that will solve all your problems, you'll probably find the opposite is true, and that actually you'll have a lot more on your plate afterwards - don't forget there's a child involved too. You can only decide what’s best by being totally honest first with yourself and then with your ex. What do you both want?
If you’re not sure, a counsellor can help you answer these questions before you make a decision that you may later regret. You can see a counsellor by yourself or as a couple. They’ve seen it all before. What they will do is use their experience and skills to help you discuss the difficult things that turn into rows when you try to discuss them yourselves. It doesn't need to cost money either - you can get couples councelling on the NHS, although you may have to wait months to get an appointment.