Don't buy the house unless you are POSITIVE it's a good financial move for you.
First of all - isn't half the down payment his? What if he takes that money?
Second - what if he flakes out and loses his job it doesn't pay child support? Will you lose your home to foreclosure?
Third - property prices are very high in many places, renting might be the better financial option. Home ownership has many hidden costs. Will you be able to afford unexpected things like a new water heater, new furnace, roof repairs? There are calculators where you can see ifvrenting or buying is the better deal in your area.
Fourth - if you don't reconcile and end up in a new relationship in a few years, will you be able to rent the house out for the payments taxes and repairs?
Don't be emotional about the decision. You might not qualify for a mortgage on your own anyway.