How do I move my farm animals?

There is no direct way to do that, however due to the game giving you so many freedoms, you can use a little trick.

If you have it, you can simply use a two-handed-staff which secondary ability sets up a Repulsion Zone. You should be able to use the repel shield to move all manner of things, including NPCs and Fluffalos to the location you want them to be.

Once you upgrade to I think the final agricultural table, you can build a relocator. The relocator sucks up passive creatures (like farm animals and the little lizards, squirrels, etc., running around, and then it beams them out anyplace you like by using the opposite button on the mouse.

If you don't have the staff like myself and only have a short distance to move them you can place a three tall barrier of any block to prevent them from going the wrong way. They also sleep at night so its a day thing and they only move around two to three tiles at time. Sometimes they will go the same direction twice so it will be a larger movement but they will go back the way they just came from 90% of the time. I have not tested with two tall tiles but I know three and four work fine. I am unsure if you can use a pet pod to pick them up or not but if you do a side quest from an npc there is a chance they will ask you to pick up some sort of wild mob. If you accept then you get a free capture pod then just deny the quest and try.

Hope that helps. Kieran