I don't think that you will be able to apply for your UK Youth Mobility visa from Portugal because in order to be eligible to apply for this type of visa from a country, other than your home one you need to have a long-term visa valid for at least 6 months. Tourist visa is not acceptable.
With regards to the processing time it depends from the consulate's availability. They are aiming to finalise YMS applications within 28 working days after receiving the full pack of the required documents.
If there is no way to travel back to Australia to apply for your visa you will be allowed to enter the UK as a visitor for a period of up to 6 months but you won't be allowed to work.