I'm assuming that you are going to pot it into a bigger pot to let it grow out a bit, in which case, you are just slip potting it (not disturbing its roots(which is fine to do now)) however if you are planing to put it into a smaller pot/bonsai dish, then you would be better to leave it till next winter. root pruning at this time of the year for most plants is a no no....
if (and this would be my suggestion) you intend to put it either into the ground, or into a grow box, do it tomorrow!

use a good quality potting mix if putting it into a grow box, and if you are putting it into the ground, prepare to have elms popping up left right and centre forever after.
in order to turn it into the tree you wish to produce, you are going to have to put it into the ground/growbox......
Just re-read your post, I would suggest that rather than an ice-cream container, you get a polystyrine box and pot it into that, elms will put out roots and thicken fairly quickly.
I also urge you to join a club (there are several around Melb) one of the joys of clubs is organised dig days where you can get more mature stock for free..
