A metal doorknob works for me usually.

A metal radiator might ground you.

Internet says to touch the screws on a light switch panel.

I too live in a hilariously dry climate in the winter and become a human lightning rod for several months at a time. Here’s what helped me: a quarter! I carry a quarter in my pocket all winter to touch to metal (I deeply hate getting shocked myself, especially the huge static charges). You’ll need something made of metal that is grounded, though. We have metal shelves or the aforementioned light switch screws. You can also look for screws on your washing machine, doorknob, dishwasher, sink, etc. Anything with a little metal should work. Then - touch the quarter to it, hear (but don’t feel) the zap, and enjoy your dog with no fear. Hope you can find something metallic somewhere in your home!

Can you touch the wall with your full palm before touching your pup and see if that helps?

If you really don't have anything metal in your house (metal sinks or any appliance with an outer metal shell that should be grounded), grab an extension cord, cut it and completely remove any cable that is not the yellow and geeen one, that is the earth cable (assuming in Australia that is the correct color scheme), expose that wire and touch it to discharge. Make sure the other cables are in no way exposed. If yoy want to be extra safe, buy a plug and only connect the earth cable.

/s of course, don't do that unless you know your way around AC power

Do you have a desktop computer? If so, and you know where the power supply is, you could touch the metal grate on that. The power supply will be earthed due to requiring a ground, and the cage itself is properly made so maintenance can be done safely by connecting an ESD wrist strap to the power supply cage.

If you don't feel or hear a shock, you have not discharged.

If you have more patience, you can wash your hands for 2 minutes and you wouldn't be statically charged. Though, that may be really cold as an after affect.

Why do you wear boots on the couch? Or indoors at all?

touch a wall with the palm of your hand for a couple of seconds.

I always get zapped when touching anything metal during the winter, so what I do is touch the drywall first before touching something I know will trigger the charge. Seems to work for me.

I usually go with the light switch/outlet screw but you said those are covered. There must be grounded metal somewhere in your house. The microwave body, a pipe or faucet, you could even get one of those grounding wrist straps that plug into the ground port on your wall socket.