How would you say 'Who loves our daughter?' As that's what I thought this said! Oops
"Kto kocha naszą córkę?"
It's the matter of what is the subject, what is the object :) The subject (Kto/Nasza córka) takes Nominative, the direct object (Kogo/Naszą córkę) takes Accusative.
How can we pick out the direct subject? Is it typically at the begining of this sentence?
Accusative. Imagine the answer to this question: "Nasza córka kocha tego chłopca." - you can easily see that "kochać" simply takes Accusative, so it's also Accusative in the question.