You can take a move action without further injuring yourself, but if you perform any standard action (or any other action deemed as strenuous, including some swift actions, such as casting a quickened spell) you take 1 point of damage after completing the act.
Emphasis mine.
Is this damage subject to DR? I'm actually quite unclear as to what DR even applies to in general, other than clear exceptions like "Spells, spell-like abilities, and energy attacks (even non-magical fire) ignore damage reduction." Like... is falling damage reduced? And so on. This feat is my primary concern for this question however.