Permanent Fel Guard Companion as any class

During the quest 'Shizz Work' in Hellfire Peninsula, you get a whistle to summon a Fel Guard Hound. I'm sure you all remember as one of the quests that involve digging through piles of... Y'know...

Once you've summoned the pet near the quest giver, it appears it will stay with you no matter where you go.

Enjoy your new pet!

While on the quest (2 of us, both with fel guards out), we had a LFD pop up, we entered and realised we still had the pet, cue curious comments from the repeated dungeons we did. At some point during the dungeons (We suspect when he dropped back to the beginning of Ramparts from the end) he lost his companion. Mine persisted the entire time. After multiple deaths and a relog, the fel guard persisted for me, and I'm now flying round Orgrimmar with it chasing me on the ground.

I'm unsure if me entering the LFD changed whether I kept the pet or not, but I figured it was worth a mention regardless.