IMDB lists the quote as, "I'm your huckleberry" but according to Val Kilmer, he said "I'm your hucklebearer."
A "huckleberry" is in 19th century slang a phrase meaning "I'm your man" or "I'll play your game." A huckle is a handle on a coffin, and hucklebearers are those who carry a coffin by the handles. Doc Holliday was supposedly saying "I'm your hucklebearer" to mean, "I'll be carrying you to your grave" as in, I am going to kill you.
Either way, it makes sense...but if Val Kilmer says he said "hucklebearer" then he should know.