If you registered PSE (I'm assuming that by "an Apple Store" you mean a physical store and not the mac app store), you can retrieve your serial number by going to adobe.com and looking for My Adobe (last time I looked it was on the upper right of the page by the search box, but it moves around). Work through the links there to find your serial number. You will need your original install media.
If it's the app store version, you just launch the app store on the new computer and go to the purchases section and you can download it to the new machine.
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Incidentally, you can never move an installed version of PSE. PSE is not a tidy package app like most mac programs and you can't ever find all the bits and bobs you would need. You must reinstall it each time.
Yes a physical store is where I bought the tablet. And thank you! I will go look for it now! (: