On whistles with heightened breath control, I find it hard to go down a whole octave between notes and still maintain a good tone and airflow. I get this bad sound that’s hard to describe, but I think you know what I mean
I have to cut short, and begin the airflow anew when I start playing the note one octave lower.
Any tips?
Also, should I practice intonation from the start when learning the whistle?
Yes … Cut the high note short, and begin the airflow anew when you start playing the note one octave lower. 
Seriously, that’s fine. It’s pretty common to articulate (tongue) the second note when doing an octave shift. Yes, you should be able to to this cleanly without articulation, too. But that’s a question of experience, practice, and good breath control.
Yes, of course. Listening to yourself carefully is always important.
Okay. I’ll guess I’ll try practicing it some time, or maybe it just comes along automatically after a certain threshold of breath control has been reached…
Okay. Should I use a tuner?
People tell me for my fiddle playing (yes, I’m learning whistle and fiddle simultaneously) that tuners are bad for training intonation, since you train the eye rather than the fingers/ears. Don’t know if that applies to whistle too…
The absolute best for pitch practice is to practice with a drone note.
Many electronic tuners can produce a reference tone - use a D or G depending on what key you are practicing - play the tunes with the drone and listen - each note should sound sweet, you will be able to hear it and adjust your note to hit the sweet-spot. After a while you will be pitching the notes naturally.
There is a lot of stuff to overcome when switching octaves - many whistles have a band of chaotic frequencies between the correct pressures required for pure, in-tune notes in the 1st and second octave using the same fingering - the trick is to hit the correct part of the pressure gradient to do the octave transition cleanly. This can be very demanding because each note and its octave has a different “chaos” band that needs to be avoided.
It gets more complex than this - intervals between each note can also have a chaotic dominant that needs to be supressed for the second note to sound cleanly. Many times it is necessary to cancel the current note to get the second note to voice.
Devices such as cuts or tongueing can serve to cancel the resonant.
Some whisltes are made to reduce this effort - some are not.
That is not a judgement on whistles:
I have observed that a whistle with a very broad chaotic break between notes can be the instrument of choice when playing airs - the additional dimension allowed by the richer harmonic sequence can be very useful for expression … but such an instrument may be useless for playing a fast reel. A whistle with very narow chaos bands is essential for playing fast aticulations necessary for standard dance-tempo tunes .. may be a bit bland playing an air.
There are very very few whistles that fit the bill for all different styles of playing - I would say probably none would do the job if you include non-ITM styles of music.
Wow! I had not thought to play with the drone note… hey! You learn something new every day! 
Thanks for that info!
Sure, drone practice is OK. But most whistles are tuned more or less to Equal Temperament (12-TET). So you have to know what you’re listening for: e.g. pure 4ths and 5ths, or tempered intervals. When playing with pipers, the flat-ish Just tuned F# and B are pitches to watch out for.
The thing is … for real playing at dance tempos, “ballpark” intonation is good enough - say, within +/- 10 cents. Tuners are no substitute for your ear, but they can be useful tools, and visual feedback is one more cue.
I like the Shakuhachi tuner (software). You can set the “blue zone” to 10 cents, and practice playing in the zone. The running pitch graph lets you see the consistency of your pitches over time. For a different view, the Flutini program shows you your average, cumulative pitches.
Shaku Tuner: http://www1.ocn.ne.jp/~tuner/tuner_e.html
Flutini: http://www.novasession.org/Flutini/