Going back to the original question, though.....
I suspect that 0:30+0:30 is the correct answer for your logbook. But watch out, because logbooks are different. Most smaller logbooks designed for PPLs that I've seen have one set of columns for day (dual/solo, single or multi engine, etc) and another identical set for night.
But my Jeppesen logbook has just one set of columns to indicate whether a flight a dual or solo, and whether it is single or multi engine. It then has just one column for night flying. I figure that in this case the correct way of filling in my logbook would be to record 1:00 as the total time (in the P1 column), and then put 0:30 in the night column.
I think, at the end of the day, it actually makes no difference as long as it's clear.
FFF
-------------