Not a "jump", not even a small one, not in Traditional Yang Family T'ai Chi Ch'uan.
Your form practice may be different if you are practicing a "Yang style" outside of the Association, so be sure to ask your teacher for clarification.
In Traditional Yang Family T'ai Chi Ch'uan this is a pivot to readjust your position relative to your opponent or opponents, done while standing on only one leg.
The movement should not be "jerky" or done out of synch with the rest of your body.
As with all other movements it should be smooth and coordinated.
This will take time to learn however, so you may feel a bit "jerky" while you learn the correct method.
Sometimes the only thing you can do is "fake it 'til you make it". Which means; do it the best you can right now and with a lot of trial and error you will eventually smooth it out.
It took me about five or six years to learn to do these kinds of pivots even half correctly, so don't get discouraged.
As for breathing during this transition; I highly recommend it.
It sure beats the alternative!
All jesting aside; just breath naturally. Don't force it or try to make your breath coordinate to your movement in any special way.