CBF – Have a look at your Strata Plan (drawing), because it’s sometimes the case that wall/s (and any windows/doors therein) adjoining a courtyard/balcony that’s part of a Lot is not Common Property.
If the wall is Common Property then in normal circumstances repairs to the glass sliding door would be the Owners Corporation’s responsibility, but is the door itself damaged or does the Owner want the entire door replaced because the type of doggy-door used necessitated cutting a hole in the glass of the original one?
If, as I suspect from your post, that’s the case, then it isn’t a normal circumstance and I’d be looking for a compromise whereby the Owners Corporation arranges and pays for the repairs (is re-glazing an option?) and then seeks a partial reimbursement from the Owner.
What happens with the dog access post the repairs?