Im going to repeat what my 85 year old mentor taught me. Do not
transplant any plant that is in bloom or trying to produce fruit.
Wait until after the plant has finished its reproduction cycle and
even then wait another month. In areas that don't have seasonal
changes, this is recommended. In areas that have cool winters,
anytime when the tree is dormant. If the tree has new buds on it,
youre too late and its best to wait till next year. The reason for
this is a plant expends all of its energy to reproduce. That's its
number one priority. If you disturb it during this time, it may not
have enough energy to recover and you can kill the plant. My friend
best described it this way: If you have a bull and a cow trying to
mate and every time they get it on, you walk up behind them and
whack the bull on the butt with a two by four, and then you wonder
why you don't get any baby calves. Its the same way with plants
that are in bloom.
In Climate Zone 5 we always transplant our peach trees in April,
preferably before the tips of the leaf buds have started turning
green. Since all of the fruiting and leaf buds are formed on the
previous year's wood(growth) transplant your peach trees before the
fruiting bud shows any pink.