Visa for gap year in Europe

The Schengen agreement (and the convention implementing it and EU regulations that replaced it) is only about short stays under three months. Whether they need a visa or not (Australian citizens do not), third-country nationals cannot stay more than three months in the Schengen area under those rules.

To stay longer, you need a national visa or residence permit. Such long-stay visas (including working holiday visas) are always issued by one country and only valid for this country. There is no such thing as a long-stay visa for the whole Schengen area.

That said,

• Time spent under the long-stay visa does not count towards the three-month limit. So you could backpack for three months, spend six months or even a year in Germany under the WHV and finally go elsewhere in the Schengen area for another three months. But not the other way around.
• There are no systematic border checks between Schengen countries and residents in a Schengen country also have the right to travel around the area for up to 90 days so you could easily visit other countries while staying in Germany on work holiday visa. Your stays in other countries would still fall under the 90-day maximum stay rule but since there would be no record of your travels and no entry/exit stamps, you could probably get away with spending a little longer than that outside of Germany.
• Some countries in Europe and around are not in the Schengen area, so it's possible to spend some time in the UK, Ireland, Cyprus, Croatia, Bulgaria, Romania, Serbia, Bosnia and Herzegovina, Albania, Montenegro, Macedonia, Morocco, Tunisia, Ukraine, Turkey, etc. between stays in the Schengen area. You can't do that indefinitely but you could probably manage it for a year, seeing other interesting places in the process.
• Several countries offer working holiday visas to Australian citizens. You could also spend some time in one or two of them, making some money between visa-free visits to the rest of the area.
• Australia still has bilateral agreements with a number of Schengen countries allowing Australian citizens to visit them even after exhausting their 90 days in the Schengen area. Using these agreements requires careful planning but that's another way to stay longer.

Whatever you do, you need to research the rules thoroughly and plan your itinerary carefully as there is no single visa that would allow citizens for non-EU/EEA countries to travel completely freely in Europe for a year.

Incidentally, there is a proposal to introduce a “touring visa”, specifically intended for trips like yours. But it's not currently part of the law.

Getting a long-stay visa from Germany will not in itself allow you to travel in the other Schengen countries more than you would otherwise be allowed to. (Since you're Australian, you don't need a visa for short stays; if your nationality had been one that needs visas, the long-stay visa would effectively also function as a multiple-entry short-stay visa for the other Schengen countries during its validity period).

However, a long-stay visa does have the effect that the time you spend in the country that issued it does not count for the 90-of-180 day short-stay Schengen clock.

So if you get a working holiday visa you will actually be able to backpack around the Schengen area for 6 months, but you need to space them out such that you comply with the "at most 90 days in any 180 day period" rule. For example, you could start by backpacking for 3 months, then stay in Germany for 4 months, and then backpack for 3 months more.

Note that since there are no internal border checks, your duty to stay in Germany for the middle 4 months is mostly by the honor system. But in order to minimize your risk of trouble, you would be wise to hold on to whatever documentation of your presence in Germany for that period you get, such as accommodation receipts or payslips.

Also remember that if you want to visit some of the EU countries outside Schengen (such as the UK or Ireland) that won't count for the 90/180 rule either.