I looked up planxty in my unabridged dictionary, and it claims that it is a harp tune in triple time that is played more slowly than a jig.

However, I have O'Neill's Music of Ireland as it was published in 1903, and in it there are planxties in 3/4, 6/8, 2/4, and 4/4.

The word Planxty is always used with a personal name, as in Planxty Toby Peyton or Planxty Nancy Vernon. So I think we can safely assume that the common impression that it means "health to" is right, and the dictionary is wrong.

The Irish word corresponding to "planxty" is "pleraca."