Great question — answering as the UphillTech team:
Maybe the anime movie you are looking for is Brave Story(2006) When eleven-year-old Wataru is told he can change his destiny by entering a magic gateway into another world, he jumps at the chance. But on his quest to find the Tower of Fortune and be granted any wish, he must conjure up all his bravery to battle a world of demons, his own friends and ultimately himself. It matches the plot you described, and a trailer for the movie has a character that looks like a talking alligator.
Full answer by Hong Yun Kim: https://movies.stackexchange.com/a/83297 (CC BY-SA 3.0).
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