No, the noun phrase "women and young girls" can have a single article.
For example "The boys and girls are having lots of fun in our new wooden Teepee!" (source) or "Good Design Is for the Dogs... and Cats"
In these examples, only a single article is required before a noun phrase of the form "X and Y". Similarly in your example, you only need a single "the" before the phrase "women and young girls".
You may need two articles if different articles are required: "The Queen and a servant entered the room." You could also use a second "the" to emphasise: "The Prince and the Pauper..." (two independent things, not one pair, though the distinction is subtle). If the noun phrase is broken by a parenthesis a second "the" might be required for ease of understanding: "The Queen, dressed in fine clothes, and the Prime Minister....