"Huckleberry" was commonly used in the 1800's in conjunction with "persimmon" as a small unit of measure. "I'm a huckleberry over your persimmon" meant "I'm just a bit better than you." As a result, "huckleberry" came to denote idiomatically two things. First, it denoted a small unit of measure, a "tad," as it were, and a person who was a huckleberry could be a small, unimportant person--usually expressed ironically in mock self-depreciation. The second and more common usage came to mean, in the words of the "Dictionary of American Slang: Second Supplemented Edition" (Crowell, 1975):
"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
February 23, 2005