The reason no one has answered your question here is that what you are asking for is below market in that area. The beaches tend to have either condos or older homes for rent. Condos tend to be pretty restrictive about pets. If they allow them at all it would be one pet, not two. Which leaves you with renting a home. Homes are going for premium prices in the Tampa Bay area these days. The only place in the Tampa Bay market area that I know of where you might be able to find a 2 or 3 bedroom / 2 bath house for under $1200 would be in the Brandon / Riverview area of Hillsborough county or Largo / Seminole / central St Petersburg in Pinellas. Brandon / Riverview the homes will be newer and more likely to rent to a tenant with two dogs. Homes in Pinellas will generally be older and less likely to rent to tenant with two dogs.
I do work with quite a few tenants and landlords. If you are still looking for a home for you and your dogs and would like some help or just to ask a few questions about the rental market in Tampa Bay, please give me a call (813) 417-3842 or send an email to Lea@LeaSellsRealEstate.com.
I promise not to bite :)
By the way, there's no cost to you for my services - the landlord's pay me!
Best of luck,
Lea Lagueux ePro, CDPE
Future Home Realty