Various charitable organizations recognize this human-animal link and strive to assure that pets, who are often de-prioritized, injured or traumatized by the events surrounding disasters, will be cared for adequately until more permanent housing arrangements can be made. The two charities I'm most familiar with are PetSmart Charities and AKC Companion Animal Recovery (CAR) Canine Support and Relief Fund. You can make donations to either fund from their web sites. Go here for PetSmart Charities, and go here for the AKC CAR Canine Support and Relief Fund.
Donations to PetSmart (either through the website or when you check out at the cash register) support the PetSmart Charities® Emergency Relief Waggin'® Program. This is a fleet of 6 tractor-trailers located at various PetSmart distributions centers throughout the US, mobilized when requests are made by animal control agencies in the impacted area. Disaster or animal rescue sites are supplied with food, crates, equipment, and experienced volunteer staff to set up an emergency animal shelter and coordinate with local shelters to assist in handling the influx of animals. PetSmart Charities has a 4-star rating from Charity Navigator, and a lot of information on their website regarding their emergency relief activities. If you donate regularly to PetSmart Charities when you check out, you'll get a year-end statement of your donations for IRS record-keeping. Much easier than saving all the receipts!
The AKC CAR Canine Support and Relief Fund is a 501(c)3 charitable fund that provides resources, funds and other assistance to support not-for-profit K-9 search and rescue organizations and pet-related disaster preparedness and relief efforts. I wasn't able to find it on Charity Navigator, but the AKC Canine Health Fund is there, with a 4-star rating. the CAR fund offers grants to kennel clubs, search and rescue organizations and rescue organizations and provides supplies during natural disasters. It is a worthy charity linked to the not-for-profit Companion Animal Recovery microchip program run by AKC.
Besides contributing to assure that other people's pets are cared for, we need to make sure we have a plan for handling our own dogs. AKC has put together a pet emergency planning guide that is a useful starting point. PetSmart also has an emergency guide at their web site that is worth review. While we have not had to evacuate our home with Hurricane Irene or Hurricane Sandy but there were times when we were without electricity for extended periods and we needed to place the dogs in safe surroundings. We were fortunate to have both a kennel and a dog-sitter able to handle our dogs, but in a widespread disaster, alternate plans would need to be made. Times like these make you realize you need to get a plan in place.