I don't see this ending well tbh

Don't buy anything or rent an apartment. Stay with you dad. Having a newborn soon and with the income you have will cause lots of problems if you get into any rental unit.
You haven't made good decisions up to this point, so don't make things any worse.

It sounds like your boyfriend needs to take things more seriously. As he's the one with debt he should get a second job to save up and pay it off. I wouldn't move in with him until he's proved he can be reliable and supportive and has cleared his debt.

If the relations between your Father and your boyfriend aren't strained, meaning they don't dislike each other, stay and save. Making a brash move will only make things worse.
Wanting your own place is normal, but don't let it darken your attitude (or his attitude) to the point that it causes stress in the situation. Show your Father that you are grateful for his help and kindness.
Focus on bringing down your debt.

With incomes like that you should easily be able to afford a place. Manage your money better.

He needs to man up. He needs to marry you, and get steady work.