Hi Beam,
Yes indeed the law was approved by the majority of ZH voters, and came into effect last year. Here is a summary:
http://www.tierimrecht.org/de/tiersc...ht/zuerich.php
And more detailed info here:
http://www.veta.zh.ch/internet/gesun.../de/hunde.html
8 breeds of dogs are now banned in Zürich. Dogs of these breeds, or any mix with a 10% DNA match to a banned breed, may no longer be imported into the canton.
Dogs of the banned breeds who were legally resident in the canton prior to the law coming into force may stay provided the owner obtains a special permit. That process was complicated, expensive, and the dog had to pass a Wesenstest. The results of the Wesenstest determine what restrictions are place on the dog (on-lead, muzzling, etc.) All banned breeds must be sterilized. Owners of banned breeds who did not apply for the permit by the deadline ran the risk of a CHF 5000 fine, or of having their dogs seized.
Fortunately, your labrador is
not a banned breed. Big sigh of relief.
However, your lab is on list 1: the big dogs. How old is your dog?
List 1 (big) dogs
born after 31 Dec. 2010 will be required to attend training classes - the type of class depends on the age of the dog. These classes are similar to the federal SKN requirement.
Do you read German? If so, you can read further about the training requirements for List 1 dogs born after 31 Dec 2010 here. Click on 'Regelment zur praktische Hundeausbildung von 1 May 2010':
http://www.veta.zh.ch/internet/gesun...e/FoundMB.html
Additionally,
All dog owners must carry liability insurance of minimum 1 mio.
There is general on-lead requirement in all public buildings, on heavily-trafficked streets, in train stations and bus/tram stops, and anywhere else so signed. A dog in estrus, a dog with an infectious illness, or any dog ordered to do so by an official must be kept on lead at all times.
Dogs are forbidden from cemeteries, from swimming beaches, from playgrounds.
Where dogs are allowed to run free, the owner is still required to pay attention to the dog at all times.
After dark, the dog must be in sight of the owner, kept at a short distance.
A dog who is known to bite must be kept muzzled.
Failure to keep a dog on lead or muzzled if required can lead to a fine of up to CHF 3000.
Failure to comply with the training classes requirements can lead to a fine of up to CHF 2000.
Failure to comply with the liability insurance requirement can lead to a fine of up to CHF 1000.
---
Now, a caveat: I don't live in canton ZH, so I do not know how the law is actually being enforced on the ground. We all know that the day-to-day reality can be quite different.

Hopefully someone who lives in ZH will come along with some first hand experience.
---
Good luck with your move - hope your dog settles in happily.