Definitely rush, although I'd suggest using archers, not warriors. With warriors, you're fighting strength 2 vs 3 (+25% city, +25% fortify) at the cost of 15 each. My estimate would be around 20% odds to win a battle. Archers cost 25 hammers, but you'd be on even odds.
While teching archery, I'd build a workboat or two, depending on how many hammers you can get in the meantime. Then you'll have plenty of food to grow and fuel working those four 1f2h tiles, soon being able to produce an archer every 3 turns.
I'm not sure how much Prince AIs prioritize archery, but since you're facing Hatty, you can expect her to go for an early religion first, she also doesn't start with hunting and is generally a peaceful opponent. Imo, waiting for archers should be safe.