By all means buy a house together but try to keep a sensible hat on.
As an unmarried couple, any more than housemates buying together, you should have a "joint tenants in common" agreement drawn up which outlines what happens if the house is sold through choice or forced sale.
You should protect your 15k so you get that back if necessary. Then any equity [additional value the house has gained] or loss [if the property loses value] should be split between the two of you. Whether that is 50:50 or proportionate to the mortgage repayments shouldered is up for discussion. Beware drafting something based on a short term mat leave which does not reflect reality down the line.
I get the impression he is currently living with you at your Mum's. Before buying/renting a home together you should establish what your income would be as a single parent and whether living together disadvantages you. It would be unfair to be expected to split the bills 50:50 if you would be financially better off without him, assuming you are not on full pay while on mat leave.
There are joint accounts and joint accounts. Some people pool salaries entirely and have a personal allowance; some people agree on a reasonable budgt and put in their share whether it's 50:50, 70:30 or whatever. If you are earning 10k and he is on 60k he's unlikely to want to live in a bedsit. Up to him to fund the improved lifestyle choice in that regard. Ditto - you don't want to get stuck with 50% of the cost of an expensive car loan for a car you don't drive or want. It works both ways and it doesn't have to be a huge battle if it's agreed up front.
The main thing that you do need to ensure that as a SAHM, you are treated fairly and not given a spending "allowance" significantly less than your partners while he has the luxury of a large disposable income.
Draw up a budget - est mortgage plus bills, then add the cost of childcare [that will be incurred when you return to work. Agree a split in principle that will apply while you are on mat leave and when you return to work. Then decide if he's worth it.
Mostly - think about what would happen if he wasn't around/turned into a deadbeat Dad. Would you move out so quickly, plan to return to work faster? Does your mum want you to move out or is she just driving you or your partner nuts. Protect yourself and your child, you haven't been together that long.
Be aware that the first 6 months are the toughest with a new child - if your relationship survives the sleep deprivation etc you'll be on firmer ground then.