A while ago I had to drill lots of 3mm holes through 12mm Nylon, so a similar situation. The problem is since the thermal conductivity of plastics is much lower than metals, most of the heat generated transfers into the drill - so the drill will soon overheat, causing the plastic to melt and ultimately break the drill. I did it by peck drilling using something close to the recommended feed-rate by G-wizard. The problem when peck drilling with a small peck depth (e.g 3mm) a significant amount of time is wasted by the drill retracting fully out of the hole which isn't required for this. So instead I substituted the drill commands for code to only retract by a small amount - for instance keep doing 3mm down, 1mm back up, 3mm down, 1mm back.. etc until the full depth is reached.
Clearly it's not worth altering the code for only a few holes or only one part, but it can save a lot of time otherwise.