Yes, I agree - a sundress (cover up or actual sundress is fine).
You can also conceal your bathings suit with a t-shirt, halter, or some other top and shorts.
Generally, no one is particularly fancy at breakfast as most are dressed for a day on the ship or shore.
I usually pack one day-time outfit for each day. I will wear it to breakfast, then change for pool (if needed). I will put that same outfit on at lunch-time; and sometimes, depending on what is planned after dinner, may wear it again at night if I want to take of my dressier clothes later in the evening.