Welcome to Tampa,
That is so exciting that you get to come to this wonderful state and Tampa is such a great location. I remember when we got orders for MacDill. I literally cried I was so happy. I am certain you will have a great time getting to enjoy all the amazing attractions, and living the Fl lifestyle during your time here.
To answer your question above, Everyone has been pretty much correct that finding a rental for a short term in this area is nearly impossible. Due to the high volume of people who only come down for the winter and spring, and the laws that make renting short-term akin to a hotel stay therefore requiring taxes to be collected (making it very expensive for an owner).
Often owners will put a limit on the size or number of dogs and with two large breeds it also may be hard. We also moved here from CO with 3 dogs one of which was a Siberian Husky. We were not able to find a rental and so we bought a home in Valrico. It is a little commute but it gave us more land for him to run and all the schools are rated A+.
I have worked with many military clients in both renting and buying. I am experienced in using the VA and USDA loans, as well as others, and can help walk you through that experience.
If you would like more information on the area, MacDill or would like to receive my free welcome packet to Tampa, just send me an email at THoyt@prutropical.com or call me at 813-352-6219.
Prudential Tropical Realty