Sure, both are good enough answers. The answers are not precise in the sense that they don't say what has or hasn't been started. But that doesn't matter. The question is vague, so the answer can be vague. This is normal conversation. A more complete answer might be "I have already started to work on them". Some more imaginative answers: "With a little time, I'll be on my way" "Hold your horses. I have all year." "I'll get going as soon as I put some finishing touches on last year's"

How are your New Year's resolutions coming along? Answer: I haven't started yet Answer 2: I've already started.