Wee - English?? Even with the quote marks round it, it's Scots surely! (Scots is now recognised in this week's census - you have to say whether you can read write, speak or understand - English, SCOTS, and/or Gaelic.)
Enjoy this! Sir Harry Lauder himself: http://www.youtube.com/watch?v=6X_3N6pcXBw
and see for lyrics:
http://www.rampantscotland.com/songs/blsongs_deoch.htm

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Lyrics copy-pasted from rampantscotland.com - Joe Offer

A convivial song from Sir Harry Lauder. Only a real Scot can properly get his tongue (and his throat) round "It's a braw bricht moonlicht nicht."

WEE DEOCH AN DORIS
(Gerald Grafton and Sir Harry Lauder)

There's a good old Scottish custom that has stood the test o'time,
It's a custom that's been carried out in every land and clime.
When brother Scots are gathered, it's aye the usual thing,
Just before we say good night, we fill our cups and sing...

Chorus
Just a wee deoch an doris, just a wee drop, that's all.
Just a wee deoch an doris afore ye gang awa.
There's a wee wifie waitin' in a wee but an ben.
If you can say, "It's a braw bricht moonlicht nicht",
Then yer a'richt, ye ken.

Now I like a man that is a man; a man that's straight and fair.
The kind of man that will and can, in all things do his share.
Och, I like a man a jolly man, the kind of man, you know,
The chap that slaps your back and says, "Jock, just before ye go..."

Chorus

Meaning of unusual words:
deoch an doris=Gaelic for a drink at the door, a last (?) farewell drink
aye=always
but and ben=a two-roomed cottage
ken=know