U.K. Youth mobility visa from Australian for 2 years expires

As pointed out in Dorothy's answer, you could leave the UK for e.g. a Schengen zone vacation.

You can avoid the problem of returning to the UK by planning to travel to Australia from a Schengen zone city. Paris is an obvious choice because it has both direct train service from London and an international airport.

No, you cannot extend this visa: explicit among the conditions of the Tier 5 Youth Mobility Scheme visa is that it cannot be extended.

However, as an Australian, you have the ability to enter many countries, either visa free or through visa waiver. As you're planning well in advance, you could explore those options, leaving the UK on schedule for nearby travels, before your partner joins you for the journey to Australia.

You could exit and re-enter the UK, although you might be challenged at the Border. Your landing interview:

• you're routinely stamped in for 6 months; after two years in the UK, girlfriend in the UK... not things in the plus column.
• you're given a temporary admission, days or several weeks; not a good thing on your record, should you ever wish to return.
• you're refused entry, removed; a really bad thing.