Huckleberry"A man; specif., the exact kind of man needed for a particular purpose. 1936: "Well, I'm your huckleberry, Mr. Haney." Tully, "Bruiser," 37. Since 1880, archaic.
The "Historical Dictionary of American Slang" which is a multivolume work, has about a third of a column of citations documenting this meaning all through the latter 19th century.
So "I'm your huckleberry" means "I'm just the man you're looking for!"
"I'm your huckleberry..." Val Kilmer as Doc Holliday in Tombstone