There should be something like "board cutout" in Eagle as well, check out their manuals. In my CAD software there is a board cutout tool, I don't have to put cutouts on the another layer, since board polygon goes to Gerber with cutouts in it automatically. However if there is no such option in Eagle (I'm using DipTrace) make sure you communicate with a PCB house and use the separate layer for cutouts, one more for assembly information, dimensions e.t.c. Just look at the design like they will do.
Don't mix up contents between layers. Silkscreen is for silkscreen only and so on.