Hi All,
Are their any simple tunes I can learn that only use one hand (left or right) in the same octave. I would like the sheet music for them too. Just trying to take it one step at a time.
My whisle is a mellow D,
All good things take time 
Bob
Mary Had a Little Lamb?
there are very few tunes you’ll be able to play with one hand…a very good starting tune is the “rakes of mallow”…also try “the blackthorn stick”
Search C&F for the Jean Duval, one handed whistle thread.
“Twelve suits in traditional style for handed whistle”
The cd has Canadian Council for the Arts on the bottom.
If you email Jean he will tell you how much to send for the sheet music.
HTH
You must be playing a different version of the Blackthorn Stick than I am.
Sandy Jasper (of Elfsong Whistles fame) wrote an “easy jig” which can be played with one hand and is available in left-hand and right-hand variations, specifically for folks just getting started on the whistle. I don’t know if she has made it available online, but you could email her and ask for an ABC of it.
There is a well-known reel by that name, too. (Not that I think he was trying to say either could be played with one-hand only…)
Hi velroc, welcome to the Whistle Forum!
I can understand that you want to proceed slowly and get a good foundation before you move on. You sound like you might be a perfectionist—I sort of recognize the symptoms. 
I think there are not many tunes you could play with just one hand. I actually think that might not be the best idea anyway, just my opinion. I think possibly doing that will make some notes easier and you may end up halting when you get to a note from the next set of notes you practiced. I would work on simple tunes and learn all the notes together, even the high ones which of course are not going to sound very good at first. You can make up some exercises to get certain notes better. But I know that I postponed working on the high notes and playing tunes with high notes in them and that became a real stumbling block. Just play whatever notes are in the tune as well as you can for the time being. It will be a long time before any of them are perfected. But you want to shepherd all your notes along together—again, just my opinion and I am a beginner.
I am just putting down a couple of tutorial websites that have instruction, simple tunes, sheet music, and slow sound recordings of the tunes. On both websites you will need to click on “Instruction” or “Tutorial” since there are several topics to choose from:
http://nigelgatherer.com/whist.html
http://www.whistleworkshop.co.uk/home.htm
Just keep at it a little bit every day. Good luck!
lol i didn’t say blackthorn stick was onehanded, just that it was relatively easy