This feels like the first time I tried to play harmonica: no control of my breathing. With all holes open, I will breathe consistent, then try to close one hole after another. The bottom three shift to an octave above. 
So, I soften my breathe, and the octave drops.
Eh, not too bad for day #2 of learning the basics, I suppose.
I should note: I am learning on a Clarke Meg.
Just keep plugging away, it takes time to get used to the slight exhale that it takes for the bottom-hand notes in the first register. Be aware that the more time you spend on that Meg in the beginning the more your ear will be trained to it’s poor intonation. They are easy blowers and can be fun since they make easy progress as a beginner instrument but they are not very well in tune to themselves.
That is where Daniel Bingamon enters the picture. 
He will make a well-tuned whistle for me to take to the next step.
I think I am beginning to understand something about the tin whistle. 
Last night, I was able to go through two octaves at least one time and keep the breath pressure correct. No octave jumping. I did a very simple succession of holes sortathing.
i am right there with you caedmon! i picked up my first whistle about a week ago, and have only had a chance to pick it up a few times. exact same issue as you, the bottom three notes F#, E, D. i had been using a Clarke Original, but succumbed to the desire of checking out other whistles already. i bought a Feadog (tricky) a Walton Little Black Whistle (nice and light), a BlackBird (on order), and a pair of Generations (by far the easiest to learn on of the bunch so far, although horribly out of tune). going back to the Clarke it does seem the most forgiving on breath control, but requires a substantially large amount of wind to play.
an exercise i am trying is starting on low D, purposely jump up an octave (first by uncovering the first left finger hole, then just through breath), down up down up, then moving to E and so on.. i have yet to be able to do this without tonguing, but it is starting to imprint in my head the required air amounts.