From what I understand, the newer models don't have a drain plug? If mine had more hours on it, I would change it out, but it looked clean when I checked it...its a wintertime project.
Should only take a cup or so to fill...I was thinking of draining it into a container to see how much is in there, then flipping the deck so the drain plug up in the air and filling to its level, that should leave at least some airspace for expansion of the fluid. Compare the two volumes...although it doesn't look to have leaked, you never know if the last guy actually filled it either.
What weight oil are you going to use? I was going to use what I have on hand: Royal Purple 85w140 or Schaeffer 75w140. I've had real good luck with both in automotive applications and in a 90* gearbox on a gravely mower deck. The oil looked like a gear oil?
My mower is sitting in the corner, patiently waiting for the snow to quit falling...