FYI, in canton ZH, liability coverage of 1 million is required.
As Sbrinz says, check with your insurer - many Privathaftpflicht policies already include dog owner liability. A few do not, though - an add-on of dog ownership liablity cover of 1 mio to an existing policy shouldn't cost much more than CHF 20-50, IIRC.
(Also, if you have a listed dog in a BSL canton, some - but not all - insurers require an additional policy.)
Since you mentioned damage insurance... Be aware that liability insurance might not cover all damage a dog could do to your flat. Insurer dependent, that might need to be included in Haushalt insurance - and even then, some require an additional policy for dogs in a rented flat.
Bottom line - check with your insurer, make sure you understand what is and what is not covered in your current policies.
By the way, here is a good summary of the Zürich law, from Tier Im Recht: http://www.tierimrecht.org/de/tiersc...ht/zuerich.php