Just applying a little common sense and some research using a birding book or the internet: Cooper's hawk adults weigh between 0.5 and 0.75 pounds. At risk of invoking unladen swallows or swallows carrying coconuts on a line, there's no way a 14 ounce bird is going to carry away (or even attack) 11 pound dog.
"I heard they had a space program, when they sing you can't hear, there's no air. Sometimes I think I kind of like that and other times I think I'm already there."
-They Might Be Giants, "She's An Angel"