I just recently got new landlord who wants me to pay back rent for a dog that I had for a while. This landlord has not been at my complex for more than a year can she cahrge me back rent for my dog if the other land lord did not and I did not sign an agreement for that year.

If pet rent wasn't in your lease at the time, I fail to see on what grounds they could collect it now, after the fact.

I have to wonder where she got the idea she even could do it. Even if your lease specified an extra payment for a pet, if the previous landlord did not collect it, then the new one has no right to.