All stuffies like that are machine done......for the face of a puppet you should not use a machine but for the rest you could get away with a machine to sew it.....I usually do the hands, neck and arms machine and the head and body by hand..I do go back to pick out the seems, however you need to be aware that the seems show more by machine no matter what than by hand sewing.....to get great straight seems you can buy a foot for the sewing machine that has a built in quider to keep the seems exactly 1/4" and keeps the material in line....they are very cheap just a nice foot to have around when sewing.  THere are other ways to rig it on your sewing machines so that you can keep the material sewn at exactly 1/4" and straight....it is simple and cheap to do but hard to explain....just google it for more details.....I will try to post some links but to busy to be able to right now.

Daryl H