OP, kindly meant but you are spectacularly naive.
Paying rent, not married, having a child, working part time?
Wake up.
You are so vulnerable.
@legalwotnot's post is something you should read and re read.
You are so so vulnerable.
There are reams of threads of desperate women, some 20 years in a relationship, unmarried, 3+ children, having raised the children, done all the housework, all the mental load, worked part time, paid for all the childrens stuff and food etc, whilst their partner paid the mortgage without their name near the deeds, to be turfed out on their ear with nowhere to go when HE ends the relationship.
You are very very naive and you had better wake up quickly.
Work fulltime.
Share the cost of childcare costs proportionally.
Do not give him rent.
If he has zero interest in marrying you, take it for granted you are always going to be very very vulnerable with a child......and start making plans to protect yourself.