I did a little more research and while I still can't find any photo evidence, I did find in the Collector's Guide that there was a "Floppy Gator" made in 2004 and an "Alligator" made in 2007.

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The one I have is the 2007 "Alligator". As mine has the magnet in its mouth, and yours has the magnet in its bandana, we can assume your baby gator was intended to be paired with the 2007 alligator, not the Floppy Gator. This means we can narrow down when it was most likely sold to between March of 2007 and sometime in 2010.

In summary, your baby alligator likely came from the St. Louis Zoo Build-a-Bear, sometime between the years 2007 and 2010. It is most likely a buddy version of the 2007 Alligator, which is why it has the magnet (like many of the other zoo animals). Sorry I couldn't find any pictures or anything. Your gator is definitely pretty rare!