Bringing a dog, cat or ferret into Germany from another EU country rests on the same three EU-wide pillars used across the bloc: an electronic microchip (or a legible tattoo applied before 3 July 2011), a rabies vaccination given at least 21 days before travel, and a valid EU pet passport recording both, confirmed by Germany's Federal Ministry of Food and Agriculture (BMEL) on its own official pet-travel guidance.
Germany also sets its own minimum age for entry: BMEL's guidance states that puppies under 15 weeks old cannot enter or transit through the country, since the earliest a primary rabies vaccine can be given is 12 weeks, plus the fixed 21-day wait before it counts — 15 weeks is simply the earliest that math allows.
The step with no real equivalent in Italy, Switzerland, the UK, France, Spain or Sweden is specific to Germany: a federal law bans bringing four named dog breeds and their crosses into the country outright, covered in its own article in this section, since it's a hard line that can turn a traveller away regardless of how complete the rest of their paperwork is.

