I Need Someone Who Knows Alot About Rabbits. Do They Carry Diseases? What Do They Eat?

My Husband Called Me Out To The Backyard Tonight & Much To My Surprise ,There Was A White Domestic Rabbit. We Caught It & Put It In A Cat Carrier. I'm Afraid To Take It To The Pound. Afraid That It Would Be Destroyed. My Husband & I Couldn't Live With That. What Kind Of Person Allows This To Happen! The Poor Thing Is Shaking So Badly That It Can't Move. Please ,Someone Out There Give Me Good Advice On What To Do. I Don't Want To Put My Current Pets In Any Kind Of Jeopardy.