CamBla

I would like to stay in Australia for as long as possible, probably via visa extension, until NVC stage is complete and I could join my partner in the US. Do you know if it's an option to undertake the latter stages i.e. the interview in Australia if the I-130 was initially applied to from within the U.K.?

The I-130 is the longest part of the of the process and you can be together in the UK whilst you're waiting for that. As others have said once NVC stage comes around your partner will need to prove that she can support you financially and may have to leave early to the US for this. Your partner could also look into a family member sponsoring you if they have enough money/income to do so. This will probably mean a few months apart, but you're unlikely to have any issues with an ESTA* if you take short visits whilst you're waiting on the latter end of the process. Luckily for you the NVC & London Embassy are quite speedy in comparison to USCIS, so it shouldn't be too long apart.
 
I understand this process is incredibly overwhelming when you first start to research it, I found this useful to break down the process: https://travel.state.gov/content/travel/en/us-visas/immigrate/the-immigrant-visa-process/step-1-submit-a-petition/step-2-begin-nvc-processing.html
 
Feel free to reach out - I have just completed this process and recently arrived to the US. I applied from the UK whilst my partner lived in the US, so the process may be a little different to you, but I am happy to help where I can
 
*do make sure to read up on ESTA's and what you can/can't do on them though. There's a whole thread in this forum of people discussing how their visits to the US went whilst awaiting their visa. You are much more likely to be scrutinized at the border with a pending immigrant visa.

Bottom line is that you cannot live in the US without first obtaining a proper visa.  You cannot live in the US during the spousal visa process, although you can make short visits at the discretion of CBP.  

You can also visit during the program if she goes back sooner to re-establish US domicile, but some time apart may happen.  The spousal visa processing can take up to 2 years from submission to visa issuance, so depending on your plan to move to the US, you can file the I130 accordingly after marriage, and you can delay the timing at the NVC stage if necessary.
 
Good Luck! 

You can stay together during the process, but she will need to qualify as your sponsor during the NVC stage.  She can qualify with a US job, liquid assets, or use a qualified joint sponsor.  SOME time apart is very common, but no need to be in the USA to start the process.

She can file the I 130 from the UK.