yesh lanu calbot (female)
also pronounced clavot. calbot is common because the singular is calbah
למה לא "שלנו".
Why not Shelanu? When do you choose of + pronoun instead of pronoun?
Because שלנו means "our" - the corresponding English phrase would be "Our dogs."
Why is "לנו יש כלבות" not an option here?
Should be. Just a way of emphasising the לנו in that sentence.