Cutting the doors.

I really want to cut my doors to reflect the radius curves on the windows that I'm going to install in the door. Essentially the door is going to be the window with a narrow frame around -- just enough to install the needed hardware. However, I'm just a little nervous about cutting that curve. A rectangle cut with 90degree corners would seem to be easier. I just got a router and it seems as though I could cut the curve on the router using the window as a template if I buy the correct bit - is there one????. Any suggestions as to the best/easiest way for me to go. If I rout the door can I use a bit that will cut right through the 3/4 inch ply without tearing up the face or backside? Any tips?
This is my window---
thanks Philip
This is my window---
thanks Philip