Can I sign my parental rights of my first child over to my boyfriend to protect her and have her covered under his insurance?

You did not mention who has legal custody of the child and what the custody arrangement is.  Also, the age of the child as been left out. What you are talking about doing does not terminate the parental rights of your child's Father, which is I think what you really want.   You would have to bring about an action to terminate his rights and have your boyfriend legally adopt her (which would also be needed for the insurance issue I am sure).  If you are not married and there is no stable home this may get you in to a court battle on many fronts: her Father and even grandparents may have the right to step in here.

There are many grounds for termination and abuse/neglect is one that you have touched on here. What you consider mistreating her and the standard of proof, however, may be very different.

You should see a lawyer very quickly to set about making a Will and plan for your children.   Good luck and a safe delivery.