Okay, not Dibdin as far as I can see.
Stuart M Frank's latest book Jolly Sailors Bold, p457 has it being sung by American sailors as part of a concert party aboard in 1842.

So my latest thoughts, there are several Minstrel songs that include the line 'So early in the morning,' but your 1831/1839 references go against this. The minstrels exploded onto the scene as groups in 1840.
BUT negro delineation was a common solo act as early as the middle of the 18thc still using the silly dialect.

If we compare it with the other similar minstrel songs I come up with a possibility of an original :-

'So earlie in de mornin' de master like his bottle-o!' Pure conjecture. Alternatively it could easily have been a genuine slave song on similar lines.