Hello, livil.s.
You are close! But your written translation is missing a couple of fada marks (like accent marks, but they govern the pronunciation of the vowel).
"Jimmy mo mhíle stór" (with fada marks on the "i" in "mhíle" and the "o" in "stór" means, "Jimmy my dearest love".
I am not familiar with the song, so I don't know how much else I can tell you at the moment. When I have some time I may check out your link and have a listen, but can't take the time at the moment.....
Dale D