From my experience playing around with dreambooth in the last few weeks generating images of a specific person or pet (not just a generic concept), it surprisingly works really well. But you have to make sure to feed it enough pictures, make sure to label the images properly, use smaller learning rate, use prior preservation loss and make sure to not overfit, etc.
For the animation stuff where you need frame to frame consistency, the new diffusion based video models show that it's possible [1][2]. These are not open source yet as far I know, but it's highly likely that we'll get them within a few months.