The White Rabbit materializes from a jigsaw puzzle and leads Betty Boop through the looking glass into Wonderland.
Vintage Betty Boop cartoon Betty in Blunderland, available to download at Internet Archive, and probably vaguely inspired on Alice in Blunderland, an iridescent dream. Not the best Betty Boop cartoon I’ve ever seen, however, it’s still amusing and it has a dodo. From Wikipedia:
Betty falls asleep doing a jigsaw puzzle of a white rabbit. She “awakes” just in time to follow the rabbit through the looking glass into a modern wonderland. Betty meets most of the traditional inhabitants of Wonderland and sings “How Do You Do” (to the tune of “Everyone Says I Love You”) to them. When the Jabberwocky steals Betty away, everyone comes to her rescue.