What's your brew setup? Gas or electric? I wouldn't do gas inside of it because of CO (the gas, not the state) and the heat.
What will be your fermentation temp control?
I brew in the garage, but the brew footprint is probably less that what you'd have in that shed, so you should be fine. But no running water will be a pain. You need water for more than the brew. I'm constantly rinsing stuff off and cleaning as I go. Maybe put in a small counter top and run a hose to a utility sink. I'd use the white RV hoses so you don't get that nasty garden hose smell/flavor on your equipment.