Dopamine is a major player for our refractory periods; the higher the dopamine the shorter the period. It's very hard to "just" raise dopamine by itself; I'd look into lowering norepinephrine (if high), which will raise dopamine in the process of being lowered. High NE is implicated in hypothyroidism and adrenal issues (low cortisol), for example.
Is there a way to get dopamine tested? How does one raise dopamine naturally?
Neurotransmitter testing is notoriously unreliable and controversial. You could get some sense of dopamine in the blood (as a hormone), which may or may not line up with neurotransmitter levels, by getting a fractionated catecholamine test, which includes dopamine, epinephrine, and norepinephrine. I've heard dopamine can be a little unreliable, but seeing high norepinephrine is a key indicator of low dopamine, seeing how the first is made from the second.
I'd look at symptoms and signs. Dopamine governs reward, pleasure, and motivation. Low dopamine creates a depression-type symptom called anhedonia, loss of pleasure in previously enjoyed activities. Sound familiar? Sometimes it's sneaky, in that you don't know how grey things are until you get a bump for whatever reason and realize by contrast that things have been grey all along.
If you want to go further on this very important neurotransmitter and catecholamine/hormone, I can't recommend Datis Kharrazian's encyclopedic Why Isn't My Brain Working?
enough, and it has a whole chapter on dopamine.