That's a tough one because the landlords are going to want to fill their vacancy right away.
If you find a rental you like, you might be able to contact the landlord anyway. It's possible they may not fill it as fast as they'd like and it could still be available later. They might own more than one property and know that another will be coming available soon. They might have a friend who has an available property.
Since you're open to a wide area - Avondale, Riverside, San Marco & St Nicolas - something should be available when you need it. You might also consider expanding your search if need be into Ortega and San Jose, maybe even as far as Mandarin.
The pets is a tough one. Landlords are often constricted by their Homeowners Insurance companies regarding the dogs......the insurance companies have made things so difficult, some landlords are being forced to refuse dogs into their homes.

You'll find someone who will rent to you with a dog, but don't limit yourself too much in your search, you might have to be willing to take a different type of rental in order to get your dog in.
Good luck, and welcome back to NEFL!
