If she produces a girl, she will be heir to the throne, according to modern royal practices, even if a male heir is born after that - far as I know. I'm not 100% sure of that, though.
After Henry VIII, his young son, who was his third child, after two daughters, became Edward VI when Henry died. He reined for six years and died of an illness. Then Henry's eldest daughter, Mary, became Queen, and was known as "Bloody Mary". When she died, from cancer, her half sister Elizabeth, became Queen. Interesting to know what the situation is, should a female heir be the first-born before a boy in the present British Royal Family.
I have watched downton Abbey until the last episode - i'm sure they'll come up with more. have just finished watching The Tudors. Fascinating! the series was filmed in Ireland, and about 50 % of the characters, especially the main characters, were Irish. It was extremely well done - but the last episode was a bit of let-down, as it finished with Henry VIII's death and just gave written titles at the end, summarizing Edward the VI, Mary Tudor and Elizabeth the First. As it had been named The Tudors, it seems like they ran out of steam by the end of the series, and finished on a rather lame note. I had loved it up to that point and would have liked it to keep going. Maybe, at some stage they will continue it.