I am quite confused.
I am given a question where $\vec p=p\hat z$ and $\vec p=p\hat x$
Where p is the dipole moment. ($\vec p=q\vec d$)
Assuming $\hat z$ is upwards, $\hat y$ is to the right, and $\hat x$ is towards us, would $\vec p=p\hat z$ be
As in, it's pointing up towards $\hat z$?
Yes. For a pair of equal charges, the dipole moment points from the negative charge to the positive one.
If in doubt, though, just use the (real) definition, $$ \mathbf p = \sum_j q_j \mathbf r_j, $$ where $\mathbf p$ is the dipole moment of a collection of charges $q_j$ at positions $\mathbf r_j$.
