Dial test indicator: dial indicator. Used to find things like edges of holes. You could also (depending on part geometry) use an edgefinder to locate the hole from the edges of the part. The drill bit suggestion will also work. Once you’re done, remember to lock the mill table in position.
Then you use an endmill (NOT repeat NOT a drill bit) to make the hole. Specifically, a center-cutting endmill, somewhat less than 1.125" (I’d say to run 0.5" or 0.75" first, but it’ll depend on what’s available). The reason is that drill bits have angled points, and will immediately try to go sideways into the hole that you already have. There’s a non-zero risk of snapping a drill bit, and a near 100% chance that the hole is ruined. Endmills have flat cutting surfaces and won’t hop into that hole.
Then you use a bigger endmill to finish the hole. Or a boring bar (essentially, a lathe cutter mounted in a fixture that allows you to slide it for really big holes on the mill).
That said, if this is to scale… That smaller hole near the side could cause you some issues, as it won’t be fully consumed by the large hole. You might want to shift left by a few thousandths of an inch if you can, to make sure you remove it completely.