Now you are beginning to understand the perils of not getting stuff settled by the court sooner.
If you want more CS than $150 a month, you will need to file for same. Since paternity is not legally established, you will have to go thru that process. Your home test kit results will mean nada to the court.
Since everyone involved is still in PA, the PA court system is where you will have to go to resolve these disputes ASAP. You could, of course, move to NY, lay low for awhile and then open a case there once you have legal residency. You would have to hope he does not seek to go to court in PA before you have a chance to establish legal residency in NY.
The courts look at the best interests of the child. However, most judges see best interest as the child being able to have a relationship with both parents. When there is distance between the parents, that can impede that relationship unless you can show the court that it will not.
If he is established as the legal father as seems likely, he will have rights. You can live wherever you choose because you are an adult. However, he can petition the court and ask that the child remain in PA, within a reasonable visitation distance or if you are bound and determined to move, he can petition for custody and you would, in essence, become the NCP who would be paying the child support, if the court granted his petition. You show that the move is in the best interest of the child and that it will NOT impede his relationship with his daughter. You had better be prepared to offer liberal visitation and pay for the travel costs, at a minimum.
If you had established the CS issue before now, it would be off the table and the move would be the only issue for the court to address. You may still be able to get what you want. Your child will soon be in school and four hour car rides every other weekend are going to get "old" pretty fast, even if you got the permission of the court to move. The type of schedule that you want probably will involve her seeing him less frequently but for a longer period with each visit. In other words, he might get a week at Xmas, six to eight weeks during the summer and maybe every other spring break (or something along those lines). Since you are the one doing the moving, you wll be liable for the transportation costs. The number of nights that he has her might be very close to what he informally has now, but this type of visitation schedule obviously is very different than what she has known before now.
So, think about how you might address his objections to the move, if he does decide to oppose it. Also, think about how you will handle holidays, etc. If you are destined for court, you might as well nail down everything that you can to avoid repeated trips to clarify some kind of ambiguity in the order, etc.