Only, Louisa doesn't call it a diary.

She calls it simply "writing" (without even a proprietary "my"), as when she says,
My candle is most out and I must give up writing for tonight. (S25)

I feel my eyes drawing together, and I think it is time to retire. So adieu to writing. (04)

At other times she speaks of her "nightly task" (013), of writing the "accounts of the day" (N1) or, simply, the day's "work" (A30).

The Manscript