Where is the Eagle component library for 0.1" breakaway headers?
Eagle does indeed. The library you will want to look for is called pinhead. It has various 2.54mm (0.1") pitch pinheaders in it.

If it's not on the list, go to the Eagle control panel window, right click on Libraries and choose Use all. Then, in the schematic window, go to Library &gt; Update all to update the libraries list.