That looks good. Add a dimension (X and Y) from outer edge to inner edge, to fully define the shape.
2mm diameter I think is pretty conservative, and if that's fine for your application, great! I've never had a problem with specifying 1mm diameter (40 mil minimum width slots). Usually somewhere in the 0.8 to 1.2mm range is the minimum they do standard, and if you ever need less, you can probably do it in a custom run.
I don't know what Eagle uses, but other tools have a PCB cutout object, or you draw a shape on the board outline layer, or something like that. For Gerber generation, generate an output for the board shape as well (layer usually being outline, or keepout or mechanical or drill drawing, one of those). Fab only sees what's on the Gerbers, so no matter how the shapes get there, make sure you have this.
Tim