Depends. If he hit the carotid, in her current rage,her blood pumping fast as fuck? She has seconds.
Tranquillising large animals always takes longer because you shoot into less well-circulated tissue from distance for safety.
Here, it's one heartbeat to the heart, ten more and it's everywhere.
Given the right dose of the right stuff, she's going under fast.
Oral anaesthesia can work within seconds. Injection will likely go even faster.