Searching for a rental home with a pet can be tough. Landlords and property managers are always going to ask the following information -
1) type of pet and number
3) size, weight
4) spade / neutered
5) and some will ask for shot records and any history of attacks / bites
You should also be prepared to pay a little more. Possibly a higher security deposit or an extra monthly fee to have the dogs. The other thing to consider is purchasing renters insurance and placing the landlord on the policy as a beneficiary. By doing this, if your dog bites anyone in the neighborhood, they will not be liable for the attack. This is especially important if the dog is on the restricted breed list that some property managers keep.
The best way to figure out how hard it is going to be to rent with your dogs is to make a few calls to available properties in the city you are moving too. Talk with the landlord and property managers and see what they say. Also be prepared to offer them references for your pets and send them pictures. Offer to bring your pet(s) to the open house. All of these things are good signs that your dog or pet is well behaved.
To best prepare yourself for a move, consider making a rental resume to share your rental information and history with your future landlords. This will open up your inventory of available properties. http://www.tenantopia.com
has a rental resume creator on their site. I have also seen on on a property manager's site here in San Francisco, but I can't recall the name. Maybe appartmentlist.