Can you download the game on a 2nd computer ??

I have Everquest 2 on my main desktop and on my laptop for when i'm out of town; can you have this game on 2 computers ??

Just download and install the game on the second machine. And get yourself a software security token to avoid the password reset prompt due to change in IP address.

http://www.finalfantasyxiv.com/playersdownload/na/

Just like TheFirstKel said, licenses for this game are per platform, but not specific to a machine, so you can play on an unlimited number of Windows machines (or PS3/4s or whatever your platform of choice may be) without having to repurchase the game or any expansions.

EDIT: also, yes if you are going to be using different IP addresses (most likely) on those accounts then a security token (physical or app) will save you a lot of trouble resetting passwords (and free teleport to boot!).