The DLC isn't actually "downloadable" content -- it's there already, always. all buying it does is unlock the content.
your DLC is attached to your account. as long as you're using the same SOE or PSN account, you will have the same DLC, same characters, and same marketplace purchases. The physical machine doesn't matter at all. it doesn't matter if you deleted and reinstalled, or bought a brand new PS3, or are playing on a friend's PS3. as long as you're signed into YOUR account, you'll have the DLC and everything else attached to your account.