Make an existing AI drawing animate to look like the head is swinging left to right

we have a AI file artwork of a (example) dog and we need the head to look like it is on a pivet at the top and it swings left to right a little bit each way

if can be done we will have a lot to do overall.

attached is a sample of a beagle in a AI file.. we need the head to move. Also a PNG file which is the final product and where the moving head needs to be moving. I added a movie file to show the type of movement needed

we have many more that need to be done as well