can a landlord say no pets under 1 year old without it being in the lease?

my fianc'e moved into an apartment a few months ago while i was deployed in iraq. pets are allowed with certain restrictions on breeds and types, but nowhere in the lease contract did it say anything about the age of the pets. i have bought a 8 week old puppy and they are saying that no pets are allowed that are less than 1 year old, we already pay a pet deposit for a cat (which as under age at the time of move in) and have no problem paying another for a second pet. are they allowed to add restrictions months after move in and lease/contract was signed?