What are your concerns?
If you want to protect your Dad's gift for you in the event of a break-up then don't get married, buy as 'tenants in common' and have a deed drawn up which says you own the deposit money and whatever percentage of the rest of the property.
This is also not a bad approach if you have you own decent earned income, your own pension, etc.
If you are a much lower earner due to childcare, have barely any pension due to same, he has savings in his name and you haven't... then you are probably better off married.
If you are not married, you definitely need wills.
If you get married you also need wills, but at least if you buy the house together, are both on the mortgage and more importantly the deeds, then you will be covered or that.
Will you take out life insurance / mortgage protection? Whether married or not.
Check who is named as a beneficiary on your respective pensions - pensions are outside the estate of your will.
My half of our house is left direct to DC - with lifetime interest to live in it for their Dad. Seen too many men inherit form a dead wife, re-marry a younger woman, leave everything to her and then she doesn't include the first children of the man in her will. (happened to 3 of my friends).
MN will telly you you MUST marry for your protection. But actually it depends on your circumstances, and what else you put on place to make sure your kids are OK. If you are a higher or equal earner and will stay that way, and have more savings / equity, you could be better off not marrying.
Which you should probably have looked at before now, if you have a child.
For example, the potential benefits of marriage to use each others' tax allowance. The need for a will, etc.