You can still get it, and it's quite easy to do (assuming they haven't decided it's an exploit and patched it out since I did it last night).
All you have to do is claim a ship you've bought on any character who can claim it. If you don't have anyone that can, discharge the one you've got and claim it again. This will unlock the Shuttle Pet for every character on your account. It should be in the Special Unlocks section, just scroll most of the way down the page.