Maybe it's just my memory but I keep thinking that I'd get an extra pet slot once my account hit two years? Am I right or do I get nothing at all?

You get a Loyalty box. Check here https://subeta.net/preferences.php

Yeah just saw the loyalty box in my inventory. I thought I had to click something somewhere but guess not. I had visited my dashboard and profile already though.

Thanks.

PS. Do we get any more on future anniversaries?

Yep, you get one every year after this too. Enjoy. :)