You are correct in that the (NSW) Schedule 2 By-Law #17 applies, and as your Plan hasn’t adopted any of the options within that, option A is the relevant provision.
Provided the equality of your voting rights with that of the other owner is on the basis of lot unit entitlement, then that owner cannot stop you from keeping a dog, but the Tribunal may do so if your dog creates a disturbance, fouls the common property, or causes any other by-law to be breached.