Andrew posted logical points and questions here.. so,
I'm not going to get into his (your BF)motives right now. Because what's important is the bond between you and your child, no matter who else enters your lives.
Your child is your main responsibility.. and we all know how relationships that go bad wind up just because we kept them 'because of the kids'.. You will not do your child a favor if you are under so much stress that you cannot concentrate on being a quality mom who's responsibility is to love, nurture and give your child a safe and warm environment to grow in.
So, which do you think is best for your child right now`? If you think that your child will never forgive you for taking someone away at this time in life, you are forgetting that a child feels the stress and will think this is the norm if you don't change it now.
Get harmony and peace of mind for the both of you as soon as possible. Childcare helps a child develop and is beneficial during the time while you work. But the quality time spent with a mom that is happy and not stressed out because of a relationship that no longer works for her is just as important during these impressionable years.
It's your choice dear, and we will be here to help you any time you need to talk and sort things out.
Good luck.

Try getting together with other single parents and share information, goals and progress. You'll see that you are not alone.