I can think of a couple of possibilities, but they are Scottish, not Irish, Gaelic. So many brown-haired girls have been the subject of lovesongs! Perhaps if you can give us a little more information, like where you heard it, and so on? Meanwhile, have a look at these links to see if either is at all close; they do at least begin with the right words, I think:

Ho Ro Mo Nighean Donn Bhòidheach
Horò Mo Nighean Donn Bhòidheach nan Gormshùil Meallach