This version was released on December 22, 2003 and was accompanied by a redesign of the website and forum (source).
This update is the one that saw Dofus Match, a fan magazine created by the community whose content took place during the end-of-year holidays of 2003 (link to the Dofus Match forum post).
A screenshot from this version is available here. Compared to v1, you can notice the addition of smileys and the sound control, which seems to have moved from the right edge to the bottom-right corner alongside the game-closing button. You can also notice the use of Mozilla Firebird, which is Mozilla Firefox before it was renamed (source).
A fight from December 30, 2003 can be seen in this video by Liche and also here; you can notice that the classes have more than 3 spells, which shows that the first 10 classes must have already been released and that development was now leaning more toward improving classes and gameplay.
In the same video by Liche, at this timestamp, on this map that will become Amakna's bank, you can notice that the building that seems to be the Dofus business office, meant to launch quests, has been moved — a screenshot of this map is available in Kam's interview from December 2003, which shows the 2 right-hand buildings swapped.
A balancing update seems to have taken place on January 8, 2004 (source).