Can she?  Obviously, yes, since she did.

Legally, can she without consequences?  No.  Report to the police AND contact the ASPCA.

Fight animal cruelty, 866-601-SPCA

What she can be charged with varies, depending on how her actions resulted in your dog's death.  For example, there is specific code addressing the injury/death of service animals, but that seems to only apply to dog owners whose dogs cause injury/death of the service animal.

Pennsylvania animal cruelty code.

The legally correct way to address your alleged nonpayment of rent is to serve you with a pay or quit notice and proceed towards the eviction process.  Destruction of property is not a legally acceptable tactic in the eviction process.