According to other users only keyboard or controller is available for now. Mouse is not available.
https://steamcommunity.com/app/1112890/discussions/0/2997674644671760742/

"You can play Calico with a mouse and keyboard", welcomes the game...
it doesn't say "with a mouse OR keyboard"

The mouse changes the view, just like the right stick on a controller. That is all moving the mouse does (well, that and wiggling animals). It would be convenient for it to work as a pointer in menus, but while remaping is possible it is controller focused and it doesn't look like there is a way to make it work as a pointer. You need to use w and s or up and down in menus, also space always works to select and enter does in some menus but not the character editor. You could remap to use only keyboard (via camera left/right instead of camera horizontal/vertical) or only mouse if you have a mouse with lots of buttons.

Also, I noticed looking at the controls remap that you can change the direction of the animal you are holding with left stick button on controller or q on keyboard and can start running right away but pushing the right stick button (no default key).

And how to rebind the keys for up or down? like [w] key.
I could rebind [q] key, but where are the other keys?

It would be so simple to use a mouse, I don't understand what the devs have in mind

Under Categories switch to default. I'm not sure why they bother to have the three different tabs when two of them are so short. I'm fairly sure what they have in mind is using a controller, but the menus are quite slow so even the controller experience isn't ideal. Or in particular minimizing the amount of platform code they need to write, at least until they see how well it sells. Most of the time it doesn't make much difference other than being unusual, but scrolling through the list of animals takes too long (but I just noticed that you can use LT/RT or scroll wheel as page up/page down there but not on the remap page or townsfolk page, although on the remap page you can move right to the scrollbar then move down or up quickly).