and that is what those peat pots are meant for... it eliminates the shock of transplanting,, you just dig a whole and drop it in,, but i would do it much before the roots start popping out,, in order for the peat to decompose properly it needs to remain damp.
just a note: different types of peat pots decompose at different rates,, the pots you have dont look like the ones i have and in fact they look like they would fall apart (or decompose) quicker than the ones i have,, i normally cut (or rip) out the bottom of the pot before i transplant as well