In the ZQuest Editor, use Quest->Graphics->Game Icons. The graphic (tile) is linked to the highest level of (Armour) Ring that Link has; and the tile bust be 4-bi (16-colour).
Note that the internal 1st->5TH quests use hardcoded tile IDs for their icons. That behaviour is likely to change in 2.55, as the quest icons should be set by the current module.