in Germany you don't need a cohabitation contract if you want to live with your girlfriend.
But you can do that, it's called 'Partnerschaftsvertrag' (English translation: partnership agreement'). You don't necessarily need a notary or a lawyer, but I would recommend to look for a legal advice. The partnership agreement is a mostly private document, it has to be considered that a few issues can't be settled in this contract.
I added a sample document as an example (German language). Detailed information in German: http://tinyurl.com/ya85dkdq