I'm curious to know what dogs have to do with the side panel on your case? If you're taking about the dogs fur being clogged up in your chassis vents then you should be looking at cases that have dust filters that you can easily remove and maintain. Fractal chassis's are a good example, as are other brands.
Now, where are you located, how much can you spend on a chassis, what are your current system's specs and what is your preferred site for purchase?
List your specs like so:
CPU:
Motherboard:
Ram:
SSD/HDD:
GPU:
PSU:
Chassis:
OS: