I was thinking and typing a different response, but then I found this.
For TBCC classic, you would need to buy this, I don’t believe your collector’s edition code would work, except another retail account.
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No, sorry. The Collector’s Edition is a bit unique in that it’s not Battle.net Account Wide. Your pet collection is, but that’s a different system that doesn’t exist on the Classic realms.
Since your Burning Crusade CE key is associated to a different WOW license than the one you use to play with, the Classic realms don’t see it and so don’t offer you the quests for the pet. 
Edit:
If you do end up activating that CE account, you’ll have the option in-game:
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Thank you for the response, super bummer but I understand that’s how it worked back in the day as well and was a choice of the devs to keep it that way. As much as the whelp meant to me I can’t justify the extra 15 dollars a month and restarting TBCC. I’m still happy I have had him on my retail account for all these years and regret starting a new license in wotlk now though >>. Thanks again!
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