You should be able to craft a tool that allows you to pick up an animal and carry it for a certain amount distance (depending on what material you used to craft it). Wood would (lawl redundancy fail?) allow you to carry the animal for a 60 block distance, stone a 132 block distance, iron a 251 block distance, gold a 33 block distance (poor gold), and diamond an unlimited distance (opposed to the normal 1562). You could craft this with a stick on the left and right side of the middle row (rows are horizontal and columns vertical [just for reference]). All along the bottom row would be the material of your choice. You would not be able to sprint with this tool, but you would be able to walk at a normal speed. In your hands, it would look as if you were holding a stick in each hand, and below the sticks would be a small bed-looking object of which ever material. When the animal was placed on the tool, a mini-model of the mob would be placed on the bed which would be looking at you. Obviously you would not be able to pick up hostile mobs. You could pick up wolves neutral and friendly, but not hostile.