Feminine version of "gentleman and a scholar"
Solution 1:
Perhaps a "learned lady" would be somewhat equivalent to "a gentleman and a scholar."
In this phrase, learned (lur-nid) is defined as:
- having great knowledge or erudition
- involving or characterized by scholarship
And a lady is:
- A well-mannered and considerate woman with high standards of proper behavior.
Solution 2:
I don't think there is an exact equivalent. The problem is that you are asking for a phrase with these incompatible connotations:
- It should be an old-fashioned idiom. (A modern phrase would not have the same ring to it: notice that it's rare to call somebody a "scholar" these days, except in a rather narrow, technical sense.)
- It should suggest that she is scholarly.
- It should suggest that she possesses the qualities admired in a lady.
They are incompatible because, traditionally, female scholarship was not considered ladylike. A female scholar was considered a kind of de-feminised monster.
Solution 3:
I can only think of one proper word for an intellectual woman: bluestocking. The etymology is given at Etymonline and Wikipedia, but as you would guess, originally the term was derisive and not appreciative. The situation is different today, for example, Chambers just states:
An intellectual woman
There is another substitute from the French: bas bleu, but the etymological connotations are the same.