Based on the facts you have described, my understanding is that you have been granted custody of the common child and you are seeking permission to move away from the area in which the non-custodial parent resides.
In order to relocate with your child outside of New York State, you would need to petition the court and obtain judicial approval of a new relocation plan. If you chose to petition the court, to obtain approval of the relocation plan, courts in New York will place primary emphasis on the rights and needs of the children. Given this reality, it is particularly important to emphasize facts that show that the move would serve the child’s best interest. You could show this by emphasizing the financial benefits of moving, family in the area, or any other factors that you believe are relevant.
Additionally, given that the father is not too involved, if possible it would be much easier if he consents to the relocation plan. This could avoid a great deal of stress and acrimony
Finally, as I have mentioned in other blog posts about relocation, where the custodial parent does move with the child to another state without the consent of the court or the non-custodial parent, it is very difficult for the court in New York to enforce the order. This is not intended to encourage you to simply leave the state without the court’s approval, but jurisdictional challenges may arise once the custodial parent leaves New York with the common child
I highly recommend you consult an attorney before going forward. These proceedings can be very emotional which makes it difficult to separate intense emotions from the relevant legal facts.