I think I most wanted to be reassured that having a twelve year old girl, even in the early part of the last century, who really didn't know what menstruation was would be believable. I didn't want readers thinking "She can't be that clueless!" I think the characterization is aided and abetted by her having no female siblings and a distant mother.
Thanks again (everyone!) for all the great responses!
Carrie by Stephen King was set in the 70s and 16 year old Carrie didn't know what was going on, and that was believable, because of how Carrie's mother was (overly controlling and deliberately isolating Carrie) and also how she was bullied and excluded at school (therefore never got the chance to hear other girls talking about periods, tampons, etc). Sixteen is also very late for periods to start, but not outside the normal range.
Because the average age of first menstruation was a bit older at the time you're talking about (closer to 14, whereas now it's closer to 12) then she would be an early starter at age 12, so it's easier to explain why she doesn't know, i.e. maybe her mother never thought that she might start that early so hasn't had the chance to explain anything to her yet.
Periods tend to come towards the end of puberty, so she'd likely have other signs of having already started puberty and be an early developer compared to her peers. She'd likely be taller and one of the first to start growing breasts, which she may be embarrassed about, especially if her mum's not discussing any of this with her. She may try to hide her breasts with baggy clothes and feel generally self-conscious. It depends on her personality how she reacts to these changes, but if she hasn't got anyone to talk to about her body changing, then she's more likely to feel self-conscious than confident or indifferent towards her body. Other signs of puberty may distress her if she doesn't know what's going on. For example she might be very disturbed by growing hair in places that she didn't know people were supposed to have hair. (It's plausible if her parents are quite puritanical and she's not so poor they all have to live in one room together that she's never seen a naked adult, or a picture or diagram.)
It is more plausible for girls to be completely clueless about periods until the day it happens back then than it is now, but it's still plausible even now, with the right circumstances. It's a matter of how you write the situation. Even back in the day, mothers with common sense would clue their daughters up about what's likely to happen, teach them how to wear and wash rags, etc, even if they tell their daughters to keep the whole thing secret and never discuss it in public. For me, I'd still need some kind of explanation for why her mother hasn't done that. Her being only 12 when she starts and her mother not realising it could start that young would be sufficient (which could be as simple as "Oh, darling, I was going to tell you. I didn't think it would happen so soon," kind of thing). Or showing that her parents/caregivers are neglectful, or some other brief explanation.