The timer’s set to 30 minutes by default, but I’m not certain if you can tweak that. No worries, though! If it shuts off, just give it a quick restart after the half-hour is up.
I’ve got a Q8 e-tron, and while it doesn’t have a specific "dog mode," I can totally fire up the climate controls from my phone, no subscription nonsense! So my pup stays cool with the AC running.