Generalization of the DL-assumption in bilinear group pair
Usually the point of working with a Type 3 pairing is exactly to have
  such a tuple, and use the pairing to decide if the fourth element
  indeed equals $zQ$ or some other element. So if this problem is not hard
  and $z$ is private, then you're in trouble.


From your explanation, I don't think you require a Discrete Log-like assumption. You are saying that the pairing is used to check if some element is indeed $zQ$ or some random value. This seem to imply that $P$, $zP$, and $Q$ are known to an adversary, and you want to ensure that an adversary cannot produce a value that passes the check you make with the pairing.

Assuming I understood this right, then this seems to be a fit for the Computational co-Diffie Hellman problem (co-CDH): given $P$, $zP \in G_1$, and $Q \in G_2$, the co-CDH problem is to output is $zQ \in G_2$. This output is what you are checking with the pairing, so it seems to me that the co-CDH problem is what you are looking for.

In this case, a Discrete Log-like assumption may be overkill, since an adversary wouldn't need to find $z$. It suffices to compute $zQ$.