I've seen literature and QuTip implementation of calculating a gate fidelity given the transformed density matrix, and in that case it uses a number of different initial states. My question however, is how should the Pauli Noise model (X,Y,Z error rate) be calculated if I have the density matrices before and after transformation?
In general, you cannot represent an arbitrary unitary operation in terms of a Pauli noise model (if you could, then you would be able to simulate it efficiently on a classical computer!). However, if you perform some circuit magic known as Pauli twirling via randomized compiling (https://arxiv.org/abs/1512.01098), you can transform your noise model into a Pauli channel.
This answer has a great summary of Pauli twirling.