Check your state/city laws and your lease CAREFULLY...breaking leases can be very expensive and if your evicted its even more costly.
I am an Apt. Manager in OK and I ALWAYS find out about illegal pets. It isn't hard, a neighbor complains about stepping in poo, the monthly pest guy does an inspection sheet that notes pets, poor housekeeping, etc. A neighbor brags about how cute your baby is, Maintenance comes in, the sources are endless and I don't have to even try. The key is whether or not a manager cares about their property and residents.
We allow pets for a $200 Non-Refundable Fee (which can be paid out) so I believe that if your willing to get and take care of a pet this is part of it. When you break that down over the course of a lease its nothing...alittle over $16/mo on a 12mo lease....just consider it "rent" I guess. I will even allow over the weight or "Viscious breed" pets if the owners can show that they aren't aggressive and are well behaved. We also have treats in the office and know most of our furchildren by name, but then again I am an animal lover.
Also consider the safety issues involved. Living in an apartment is living with lots of strangers...lets say a fire starts in the building, here the police dept has #s for all apt managers and we are called. If the fire dept is evacuating the building they will want to know how many people live in each apt and if there are pets....if they don't know about your baby they wont know to look for them. I know this is far fetched and don't mean to scare you but it is an example of "worst case" consequences. There is so much more involved than just money or "getting one over" on your landlord and its not fair for either of you to have to walk on eggshells in your own home.
Get a copy of EVERYTHING you signed and read it so you will know what your up against. If you need any further info feel free to PM me, the laws are different state to state but I can help you understand the terminology involved in your lease.
Best of Luck!