A few bits of key information:

There is no status match with Qantas. They basically don't offer it to anyone except in specific corporate deals etc or when something exceptional happens (relocation isn't one of them).

Qantas equivalent of BA Gold is Platinum.

BA does not allow an Australian address to be used for the membership so you will need to keep your membership in the UK.

There is no BA-branded credit card in Australia. There is no Avios-earning supermarkets in Australia, either.

Earn rates are different between the two programmes but Qantas, by and large, have a worse burn rate, and the cash components on Qantas flights using Qantas points are far larger than those booked using BA Avios (as are the burn, although not as substantial). The difference in some cases can be up to 500% as I recently found much to my amusement.

Ease of using Avios if redeeming on any OW flights is basically no different between the two programmes unless you are using Gold Priority Reward on BA, or you are a GGL, or Qantas Platinum 1 (which is NOT the standard Platinum 1 and the bar is set much higher), none of which currently applies to your case, so you might not even notice any difference (with the exception that JL flights cannot be booked online using Qantas website - it just doesn't work, and usually call centres can't see them either, whereas there is no such problem with BA, normally).

However, Qantas points offer points and cash bookings etc. on Qantas flights so that may be attractive if you are planning to use Qantas points on Qantas flights but may not have enough points to pay for it (it basically works as a discount on a flight).

I think you need to look at your individual flying patterns, decide what your priorities are (status or points), and how you want to burn the points, look into what cash components you are happy with etc.

There is no one size fits all programme that works for everyone, so each person needs to read up the programme in detail (and I mean in detail), consider how they will earn and burn, before making a decision.