first of all: Yep, you friggin' nailed it!! lol..that is a great pet-portrait and - I'm sure - EXACTLY how the dog's human would like to remember him 30 years from now
Value is about PERCEPTION: how much time did you spend with the dawg? How much time did you spend selecting, cropping, post-processing? Are you providing him with the original full-rez file?
Do you want this customer to come back when something else of significance happens in his life? Kids' birthdays, new pets, etc. ? Are you going to pitch more to him - how about a friend-shoot? How about a portrait session with him AND the dog? How about a session with him?
Think salesmanship: you can offer him one price if he will give you more business and another price if it's a one-off, for example?
Blow him away and provide a $4 12X18 inch blow-up from Costco! No matter what he choose...just throw it in there...see what he thinks....
Heck, give it as a freebie and say it was your pleasure to shoot his beautiful dog and ask him to consider you for future work...
...in short: be creative and think longer term. The BEST marketing in the world for someone in your position, is to break into social circles. He will take that 12X18 inch print to work and show it, he will show his friends, he might even frame it and hang it on his wall and everyone sees it....
Forget "profit" for one picture and go ball-to-the-walls with the salesmanship, is my advice. That's how I've gotten numerous paid gigs of events that my customers would NEVER have thought to PURCHASE photography services for