I think it's $2.00 for the first eighth of a mile and $.25 for each eighth after that; but you could do a search for the Orlando airport, then find the transportation page. There should be taxi rates there, and that will tell you what the general charge would be.
Two other options: Call the Doubletree
Budget counter and see if they have some type of transportation; or take the Pop bus to Downtown Disney and get a cab there. Hotel Plaza Boulevard is only a mile long, it can't cost you more than $5.00 with tip (includes getting through/out of the DD parking lot, along with wait time at traffic lights).