Discussion of pregnancy in print during the early 19th century was almost wholly restricted to medical texts. These were extremely clinical, intended for the growing population of male obstetricians who were pushing midwives out of the birthing room, and are unlikely to have been read by the average woman. Outside of the pages of these books, pregnancy and menstruation were rarely referred to explicitly, and appear to have largely discussed through what seems today like extremely vague euphemisms. As a result, in many cases they have been badly misunderstood ("confinement" meant labor, but many have taken it to mean that women were confined to their rooms during the whole pregnancy or the last two trimesters) or simply missed. Among midwives and women who were seeking to end a pregnancy, the cause of a missed period was referred to as a "blockage"; you would go to a midwife to deal with this blockage rather than saying, "I'm seeking an abortion". Later in the century, those who could help with the problem used the phrase "menstrual irregularities" or similar in their advertisements. The pregnancy was not considered to have truly begun until the quickening, when the fetus began to move in the womb, and abortions before quickening were typically de facto not seen as much of an issue.

One of the few discussions not restricted to medical journals and texts for doctors can be found in The Female's Friend, and General Domestic Adviser (1837). Here's how that book describes the symptoms of pregnancy:

The symptoms of pregnancy are easy to be discovered: a revolution in the female system so great, must be attended with strong indications. The most common symptoms are as follow: - sickness of the stomach, and vomiting, which is more apt to come on in the morning and after meals, than at any other time; toothache; heartburn; a peculiar change of countenance; occasional headache, fretfulness and peevishness, quickness of pulse, hurried breathing, antipathies, and longings; the mammae from the natural colour to brown, and a cessation of the natural periodical affection takes place. These are the most usual symptoms, but they may not all be present at one time; the most frequent and almost never failing symptoms, are, sickness at the stomach, change of colour in the mammae, and the cessation already alluded to.

(Note that the book also talks about taking "steel powder" to help with obstructions of the menses, and things to eat "to promote the menses". More clinical vocabulary, but still talking around the issue itself!)

So there's a balance here - on the one hand, women did recognize that a skipped period indicated the presence or future presence (depending on definition) of a pregnancy and that the early stages were when it needed to be taken care of, but the skipped period was also not considered the sign of pregnancy. Given these standards and the general discretion around referring to pregnancy, it's possible that a woman would not refer to her "interesting condition" - another contemporary euphemism - with most people until she began to show and/or felt the quickening; if she noticed her late period before any other symptoms and was inclined to talk about it with people she was on very intimate terms with, she was highly unlikely to say, "I'm late" (that simply wasn't a standard phrase that others would understand), but she might refer in a vague way to the fact that certain natural processes had not happened for X amount of time. I'm not really sure what you mean about demand being in the mixture re: "I'm late," but if your character is speaking to her husband, it would probably make the most sense for her to say that she is "with child", or that she will soon be a mother.