Next, let's think once more about whether we have time to take care of a dog.
Literal
Next we [to-に] dog [possessive-の] care [object-を] do time [subject-が] exist [question-か] once-more think-[tentative-てみましょう].
犬の世話をする 'to take care of a dog.' 今一度 'once more, one more time' is a slightly formal expression. ~てみましょう 'let's try doing' suggests a collaborative reflection. The sentence addresses a family considering pet ownership.