Your link says you can make it colorfast, but then says it has to be washed on gentle or dry cleaned. This is a baby quilt. It will get washed repeatedly.
So, I would cut the Boston Terrier out of the panel and use the rest somewhere else.
https://www.fabric.com/buy/0467084/d...35-panel-cream
https://www.fabric.com/buy/0467102/a...23-panel-cream
These may be to "cartoony" for you, but there are lots of choices.
https://www.etsy.com/search?q=boston%20terrier%20fabric
bk