your teacher will probably get pissed off if you don't, because they have to clarify that you do research regularly etc. So if she/he's picky, then date your journal because you might lose marks that way.
But you won't get marks taken off for it at the marking centre. They don't look at your journal until there are some inconsistancies, or something unusual, like plagerism etc.
Girl got 50/50, never dated her journal. It's all good.