I'm curious as to what about this would be a punishment? Like, does your pet have a humiliation kink that you've covered with each other? If so, is humiliation on the table as a punishment? If so, is she even embarrassed enough by any of the porn she's watched that this particular humiliation punishment would be effective?

All that aside, from looking at your responses to other comments, it doesn't seem like punishment is really what you're looking for here. Your pet has challenged you to be a stricter Owner and you're wanting to rise to the occasion. Punishments are for breaking a rule, which she hasn't done. It sounds like what you're looking for is ways to train your pet. And, yeah, this might do that if you're both into it.

But so might anything else. From your telling of things, what she wants is for you to dominate her, and to do so more strictly and intensely than you've done so far. The specifics aren't all that important. Just lean into your shared kinks and be ever more demanding til you find the level that works for the two of you.

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(sidebar: when someone says "My first ___" about their current partner it always makes me laugh a little.)