Pretty sure Moss Landing has a wait list for assigned berths (I'm on it), and you have to have an assigned berth to live aboard. Last I checked, the wait time was 12-14 months.
It is true that they have transient berths available with no wait, and could accommodate your boat
(but not you) until you got your assigned berth.
They do allow pets
for a very nominal fee (something like $5/month).