
Action Economist |

Let's see...
When worn, this simple brown robe confers great ability in unarmed combat. If the wearer has levels in monk, her AC and unarmed damage is treated as a monk of five levels higher. If donned by a character with the Stunning Fist feat, the robe lets her make one additional stunning attack per day. If the character is not a monk, she gains the AC and unarmed damage of a 5th-Level monk (although she does not add her Wisdom bonus to her AC). This AC bonus functions just like the monk's AC bonus.
At 2nd level, the cavalier does not provoke attacks of opportunity when she attacks foes while unarmed so long as she is dealing nonlethal damage. In addition, the cavalier's unarmed strikes deal more nonlethal damage than usual; she is treated as having a number of monk levels equal to her cavalier level for the purpose of determining how much nonlethal damage her unarmed strikes deal.
For example, a 12th-level cavalier of the order of the hammer would deal 2d6 points of nonlethal damage with her unarmed strike. The cavalier must still select the Improved Unarmed Strike feat if she wants to deal lethal damage with her unarmed strike, and lethal damage dealt with her unarmed strike is not increased by this ability.
It appears the Monk's Robe doesn't increase the damage as the Cavalier doesn't count as having any levels in monk that are applicable for applying the effects of wondrous items. It DOES seem that the Cavalier would gain the damage of 5th level unarmed strikes from the item though, but that wouldn't be useful by the time you got a Monk's Robe.
If the Cavalier does gain any levels in monk, the situation is a bit sketchier. It seems her Monk levels and Cavalier levels WOULD stack when dealing damage with her unarmed strikes since the table indicates the damage is based on monk level. It would also mean that the robe WOULD increase the damage by increasing her effective Monk level. However, the rules on this are kind of wonky and you might just use the higher of the two effective Monk levels for determining damage.
TL;DR: The damage wouldn't increase if the character is a pure Cavalier but they would increase if the Cavalier had any levels in monk (probably).