In case you want to spend some time window shopping, having a Iced Latte, but you need to take care of you dog, go to K-Ville. It is a dog friendly shopping place. They offer poo bags and a dog toilet. Not sure if you can enter the shops with dogs, but the public area in the ground floor is open for dogs - on a leash of course.
I also saw signs at the Paradise Park shopping mall that in certain areas inside dogs are not allowed, what brought me to the conclusion that in general dogs are ok. But better ask before.