This is actually a great policy for a shelter in NY. They allowed your dog to get all the way to 12 months before requiring the dog to be spayed/neutered. That allows the dog's growth plates to close and to have his nads for growth and maturation. Nice. A lot of shelters will spay/neuter -- their vets -- lots of partial spays and material left behind in some of these places, and they do it before you pick your dog up. I mean, they do not do the operation, let the dog heal and then put it out for adoption, because they will be operating on dogs that will just be euthanized anyway. So, they wait until you pay the money, and then they tell you to pick the dog up tomorrow, sick from the surgery. Fine. Sometimes this is at 8 weeks of age. Not so fine.
Shelters are in a position of dealing with pets no one wants, and a lot of them do not get adopted and must be euthanized. For them to spay/neuter before they go to their new home, or to sell them on a spay/neuter contract is understandable, reasonable, acceptable. The alternative is just to euthanize them all. If you get a dog from a shelter or rescue, expect it to be altered, or to buy on that contract.
Most states have laws requiring state-run shelters to either spay/neuter all animals before selling them, or to require it to be done by a certain date.
Knowing the law is your responsibility. It is NOT a state-wide spay/neuter requirement, though there are some states that have tried that or are doing that, with only some exemptions. It is for dogs already landed on the public dime -- it is the right thing to do.
In the paperwork you received when you got the dog, there was probably a paper that was signed by your gf that agreed to the altering of the dog. I cannot believe you all did not sign this. Go back through the stuff.
If you made that agreement when you took the dog, or if you agreed to abide by the state laws with respect to the dog, than make an appointment and get your dog fixed. It IS the responsible thing to do, because you got your dog from a shelter or rescue.
Our shelter used to provide a voucher to people for altering their dog. Great right, they could let their pet get full grown and then alter it. So few people took advantage, and so many bitches were turned in that had been adopted out with that system, pregnant or with puppies, that they changed it to spay/neuter before you take it home. Not being responsible and doing what you agreed to do will hurt other dogs down the line, who will not be able to mature properly, being given pediatric spay/neuter because people simply will not abide by what they said they would do.
Fix your dog.