There's also two McDonalds on the A689 dual carriageway as you come into town, one near the Historic Quay at the marina, opposite Asda (opens at 6am), and another opposite Tesco on Burn Road roundabout, this one opens at 5am. No more than two minute drive from the marina at that time of day.
I can vouch for the McDonalds breakfasts being nice, although you need two to fill you up...lol
Not sure the supermarket cafes' will be open then, although you can always buy food in the supermarket I guess. I think the Old West Quay (a Brewers Fayre pub) will also be open then, as I know they do breakfasts, as they serve the Premier Travel Inn next door as well as the public. It's nice in there, we often go for a meal there.