Q: When is it OK to place the subject in the middle of a picture?

A: Whenever you feel that it works best!

The general rule of not centering your subject is time-honored, and comes from one basic idea: the center of an image is a stable, straightforward place. When you put something there visually, it stays there visually, usually resulting in a static composition.

When you have your subject off-center, you can use tension and dynamic balance, which tend to make a more engaging composition.

Other factors can contribute to this: the lines from the subject's eyes and the way the subject is facing; color weight; other objects and motion in the composition and their balance. Overall, these can add dynamic interest even if your main subject is static.

You may, though, want the simple, straightforward, and more-static image. That's okay. Think about the flow of interest as you are observing the photo, and decide if a centered or dynamically-balanced composition fits your intent better.

In your particular example, the dog's face (and particularly eyes) aren't actually centered at all: they're quite towards the top of the frame. The overall subject is centered, but the face has considerable off-center visual weight. The leaves on the right side contrasting with the bright yellow flowers on the center-right provide some reason to keep the horizontal as it is; a tighter crop either cuts out the context of the plants or leaves the frame feeling cluttered.