You could try and announce in a weekly free newspaper like Kurz & Fündig or the online version, Quoka.de. Or various online classifieds such as the German ebay or dhd24 or what else is there? Just say that you are offering your services as house/apartment sitter and dog sitter and you have references and then your contact details..
I can't imagine that there won't be anyone interested in the whole of Berlin but people here in this community are generally on the cautious side (as ReallyRed said) and don't trust just anyone with their dogs even less than their homes, I would imagine. Personally, I tend to believe you, but I don't have anything for you to sit
With contracts it sounds quite good actually, that site. Though I couldn't find anything about that at first sight (not even in the FAQs), so they might want to update their page makes it difficult for cautious German people to try it out.
PS: Hm. If you're less about actual house sitting and just want to work with dogs, you could also stay in a hostel and help out in a local shelter, as has been suggested?
PPS: Still googled (the concept hooked me). Apparently in Germany such house sitting is done a little differently, they rather rent out the apartment for the time of the vacation. So it seems to be the other way round, you would be expected to pay rent, not to get paid for watching the house.
Sometimes there are such announcements at portals where you can also find apartments to rent, like http://www.wg-gesucht.de or http://www.immowelt24.de but I'm not sure how you could find them, can you navigate around German sites? Then look for "befristete Miete" (temporary rent).