I vote for the Mia Bella Boutique. Dog fashion is very lucrative right now, with markets growing, and your primary customers are going to be fashion-minded women... Mia Bella sounds luxe
I'm a web designer who does online stores all of the time, so I've had to help people plenty of times deciding on what name might be best for their business. I think Dawg'On Cute is very cute, but Mia Bella Boutique will probably have a better shot at attracting customers! Hope this helps a bit!