Arrivals lounge SYD?
 

There's no arrivals lounge facility at Sydney.
You can either treck across to the domestic terminal (effectively a separate airport on the other side of the airfield) where you can access the QF lounges. You're able to go airside there without an onward boarding pass. You'll need to retain your F boarding pass to SYD for lounge access under one world rules. I know there are transit busses to domestic but not sure if you need to show your onward reservation. The alternative rail link is expensive for the short journey. Otherwise, if this does not appeal there is a Rydges Hotel immediately opposite the International Terminal where you can book a day room. The day room rates are usually pretty reasonable. The treck over to domestic IMO really isn't worth the hassle unless you really need to go there. I'd be looking at the hotel day room as the most comfortable option.

Pretty sure there are no free arrivals lounges for BA pax flying any cabin or of any status outside the UK.

There are actually precious few arrivals lounges anywhere in the world, for anyone.

And some that used to exist have closed. For example, BA used to have one at JNB, but that's long gone. A handler opened a pay lounge, open to all, a couple of years back, but that only lasted about a year before it closed.

So if you're going to make assumptions about arrivals lounges, the safer assumption is always that there won't be one. It's then a pleasant surprise when that proves to be wrong.

Strictly speaking you cannot access the QF domestic lounge after arriving on a BA flight unless you are departing on another OW flight that day (which can be an international flight).

While you can go airside without a boarding pass at Australian domestic airports, you wouldn't normally be able to get into the lounge.

The exception is for Qantas Platinum or Platinum One but arriving on a BA flight may not be covered even with that.

You do need to show your onward domestic boarding pass (which is scanned) or at least an onward booking.

There is a free bus.

This would be the most sensible option.

Agreed, to the extent that I would avoid SYD transit as much as I possibly can (although DOM-INT is worse, esp. on separate tickets).

In addition, the OP would have a problem with storing the luggage if he/she has checked baggage, as he/she would not be able to get through domestic security with it. Baggage storage is rather expensive at SYD, and involve extra walking with baggage.

In fact I'd probably save the hassle of changing hotels and book where I would be staying at from the night before, and let them know that I wouldn't be turning up until the morning (alternatively, if you have Your 24 hours under SPG you can ask to check in very early, or if you are a Royal Ambassador with IHG, you can ask for 8 am check-in, and other hotel schemes may have a similar arrangement).

Why would you assume there would be a oneworld arrival lounge and also why not go to your hotel for shower.

The flight arrives early-ish in the morning and the poster probably cant check in to his hotel room until later in the day.

Why not make do with a shower in SIN? Any benefits of a shower at SYD are likely to be eroded by a rush-hour train-ride downtown, and the last I heard was that there was a sever water shortage in New South Wales.

NSW is in drought but that is not affecting everyday life. The drought is affecting agriculture significantly but we are not yet like Cape Town. In fact the local councils are still watering their greens and flowers where I am.

You just have to ask yourself: How many can I name that do? :)

My suggestion is that you do what I always do on arrival early morning in the Southern Hemisphere: book the hotel from the night before. And it's a good idea to email them that you'll be arriving about 7am and want to go straight to the room.

That way, you can unpack and shower before going out to breakfast/coffee and enjoy the day in the sunshine.