If you try to adopt a pet with Walter he will not do it saying that Woby will be jealous, but if you start with a different character, adopt a critter and then change characters to Walter (in the same world using the upgraded Florid Postern) you will keep the critter of the last character, and like that having Woby and an extra critter. I'm not sure if this is intended because Woby and the critter keep running at each other to get to the same place, but maybe it is.
1 - Start a world with other Character besides Walter
2 - Adopt a Critter
3 - Upgrade the Florid Postern in order to be able to change characters
4 - Change your character to Walter
5 - Walter appears with Woby and keeps the critter from the last character