Paper size was very variable, so there's no firm answer. However for a written-only journal it would probably be an octavo or smaller binding simply for compactness' sake and ease of use without a writing surface. The sizes would have varied, but an octavo was approximately the height and width of a mass market paperback (thickness, of course, varied). For anyone not carrying all their own gear (sailors, aristocrats with porters, etc), they would have wanted bigger pages, especially for maps and sketches, so it would have been about the size of a modern sheet of printer/typewriter paper.

One good example are the various notebooks carried by the Lewis and Clark expedition in 1804-1806. They carried a number of 4in x 6in notebooks (approx 10cm x 15cm) with many loose pages. accompanying.