Can you apply for visa not from your home country?
Applications for other types of entry clearance should be made in the country in which you are living or have residence in. Applications for entry clearance under Global Talent or Youth Mobility Scheme routes must also be made in countries or territories where you have permission to be there for more than 6 months.
https://www.gov.uk/government/publications/where-to-apply-ecb05/ecb5-where-to-apply-the-policy
As you can see, you may apply for YMV from any country as long as you have permission/a visa to be there for more than 6 months. This is helpful, but most countries in Europe only permit you to visit without a visa for up to 90 days (most) or 6 months (a minority). Which is not more than 6 months. The exception is Georgia: you can visit there for up to 12 months without a visa and so you could apply for YMS for there, but it probably isn't in your travel plans.
https://www.smartraveller.gov.au/destinations/europe/georgia
Alternatively, Australia has working holiday visa agreements with many countries besides the UK. You could apply for a working holiday visa in one of those countries, and then apply for your YMS visa from there. All of the working holiday visas have different requirements and costs and rules on where you can apply from (some only permit applications from Australia for example). You can research this yourself.
https://immi.homeaffairs.gov.au/what-we-do/whm-program/working-holidays-for-australians/work-and-holidays
