Apollo could tell that Ate was unhappy at having lost potential fun, even if it was simply a dog. He didn't want her to feel put out, so glancing around he looked for an alternative. "If it pleases you we could find a small doe and take her down, mauling her in such a way it looks as though a rabid beast attacked. Then we could leave it outside the nymph's house and wait for her to investigate."
That could serve two purposes; working out some of Ate's aggression and drawing out their true prey. He waited to see his sister's reaction, knowing that she might find a way to improve upon his idea. He assumed, once Daphne's door was opened they could gain access to the house, escalating their fun by starting a more dangerous game.