I was doing a search for this song and found this thread, but the version I'm looking for is the one recorded by Altan and also by Danu.
The frog is never mentioned in their versions, but it is clearly the the courting song.
The chorus is the part I need.
First verse goes:

Uncle Rat went out to ride
Kitty alone, kitty alone
Uncle Rat went out to ride
Kitty alone and I
Uncle Rat went out to ride
Sword and buckle by his side
(to me cax ma kerry ..... can't really make out any of this chorus!)

Other verses:
Lady Mouse will you marry me
Ask my Uncle Rat said she

Uncle Rat will I marry Lady Mouse
Yes kind sir and half my house

Lady Mouse where will the wedding be
Ask my Uncle Rat said she

Uncle Rat where will the wedding be
Up at the top of a holly tree.

Any help would be appreciated.
Bekki