Maybe. But it’s important to realize that the ability to move is not tied to whether or not you receive child support. You may be able to move, even though you are receiving child support from the other parent. Conversely, you may be prevented from moving, even if you are not receiving any child support.
Instead, the entitlement (or prohibition) is tied to: 1) how it affects the other parent’s access to the child; and 2) whether it is in the best interests of the child.
If you are the primary caregiver, you can generally move with your child as long as it does not affect the other parent’s access right. But if it does, then either you need to obtain the other parent’s consent, or else you need to obtain a court order. If the latter, then you have to prove to the court that the move will serve the child’s best interests.