will my copied iPhoto Library show up in the other/new macbook?
After connecting the drive to the new Mac click the copied iPhoto library in the Finder to open it in iPhoto.
If you want to use the iPhoto library on both macs, you need the same version of iPhoto on both macs. I assume, your new mac will come with iPhoto 9.5.1 and Mavericks. Does your current Mac support this software? Once you open the library in a newer version of iPhoto, it will no longer be readable by an older iPhoto version.
And the external drive you are using to transfer the library needs to be formatted MacOS Extended (Journaled). Have you checked the formatting? (see: Format external drives to Mac OS Extended before using with Aperture or iPhoto) If the format is wrong, you have to move the iPhoto library somewhere else, before reformatting, because formatting will erase the drive.
-- Léonie