To claim anyone as a dependent, you must have provided more than half the cost of their support, and for anyone other than your parents or a college student, they must have lived with you more than six months of the year (all year for qualifying relatives). The cost of her health insurance is only part of the equation. The rules for claiming dependents are below.
Your boyfriend's back child support would not affect your taxes, if that is your concern. If you were married, they would.