this illustrates the idea of morphing between two images.
https://www.youtube.com/watch?v=rz0TZzQhDgU
in essence there are two versions of each of the various components (hair, eyes , nose ...) - one for Albert and one for Marilyn - and one is faded in over the other. The challenge is to get them sufficiently well aligned so that the transition works adequately well. And, ofc, they're not moving!!
(In the Albert / Marilyn example, the transition is actually achieved using an animated mask to create a slow "wipe/iris" reveal - but simply using layer opacity, or even a straight switch, might work well enough for your needs.)
You could use the same basic cross-fade / switch technique with the image layers that are in the two library dogs as it seems that they're both based on the same structure. The challenge you'll face is that the riggings are different and there are subtle differences in layer placement - so, for example, simply switching between tails whilst the dogs are moving won't give a seamless transition especially where the tail joins the body. So my instinctive reaction would be to use the sheppy rig and add the husky images to that and go for a combination of image cross-fade and animation change (e.g. the tails both have 3 bones - the husky's curl up; sheppy's are straighter -- so maybe transition to a curled sheppy tail then straighten it out... etc etc)
There's more about assigning a subset of bones to control a layer in the (moho 12) tutorial manual section 3.5
hth
(and welcome to the forum!!)
I can use the character generator to create a person walking a dog, then complete the picture with the caption of "Pick up after your dog". However so that the person or dog combination does not look specific and that it applies to everyone having the dog and person transition from one to another would not only look better but enhance the message and provide a change throughout the animation.