Women did not live a public life in those days. They spent their time in the home of either their father or husband and had no rights - only the man could instigate divorce. Women were merely chattels. The usual age of betrothal was 12 and the couple would marry officially a year later, with the prospective husband providing financially for his future wife during this time. Sex was banned and even in marriage was limited to certain times in the womans menstrual cycle . If a girl of that age, with the restrictions that were in place over her appearance outside the home (only allowed if she was accompanied by a male) was found to be with child, then it was highly likely to be by someone in her home, and at the age of 12, even today, it is classed as rape and of course it was the woman who would be shamed by it.
To imagine a young girl of 12 in those circumstances sneaking out to have sex with a male is just too preposterous to imagine, having all possibilities of having a `boyfriend` out of bounds and as much so to imagine a girl of that age travelling alone to visit her cousin and who scripture says was told by an angel Behold thy cousin Elizabeth , she ALSO hath conceived a son in her old age Luke 1:36.
Putting things together, if Elizabeth was post menopausal, then her cousin was likely of a similar age group, though I judge that Mary was not as old. Her still remaing unmarried could possibly be because the normal marriage arrangements had not occured with her for some reason. Maybe her mother died young and she was kept on to look after her siblings. I guess her to be about 40 but of course cannot prove it. I am just reading between the lines not having enough knowledge of the customs of that time to do more than guess about this.. But anyway, it would suit the purposes of God.
Regarding the journey to Egypt, I just do not believe that God would leave a young girl with of that age without feminine help at a late stage of pregnancy with only a man without any experience of the needs of that condition, to give assistance . An older woman however would have seen it many times amongst her relatives, and would therefore not be left in ignorance or in danger of such a huge temptation to worry, the occasion of that being so harmful to the foetus.
My expereince of the workings of God is that He allows the natural laws He has set up to take place but intervenes at times but does not place children in impossible situations, or even adults, in order to fulfill His will, without lengthy periods of preparation involving suffering.
Mary speaks and acts as a mature woman not as a girl of 12 at that time.
Sorry if you dont like your long term beliefs challenged but I cant see any evidence for the claim that she was a typical early teens Jewish girl of possibly 12-13 years of age (most were this age from what I have read) there are just too many issues that go against it though of course a young pretty girl makes nicer statues. Maybe she was very ugly and that is why she remained unmarried for so long.
The response of the innkeepers is strange too - who would be so heartless to refuse help to such a sight as a young girl ready to deliver but the sight of a mature woman - well - who knows what sort of people that wouild be .