It is an interesting choice to select Gwendolen as a character that would impact Oscar Wilde's play The Importance of Being Earnest. This is because Gwendolen's role is to channel Wilde's idea that all women are superficial, annoying, ludicrous, and bratty.
Gwendolen represents the younger aristocrat, whose morals, ideals, and self-serving ways come directly from their equally haughty parents. Far from a meek and subservient woman, Gwendolen shows us a side of womanhood seldom exposed in comedies of manners: She can be frivolous- She speaks to Jack in clear terms about she "may marry often", and how she expects to "develop in many directions". All these are insinuations of a girl who does not take marriage as a sacred institution but,instead, as an activity that requires multiple attempts. Furthermore, Gwendolen is also inspired by the name of Ernest to the point that it is the main reason why she falls in love with him.
Finally, we could say that Gwendolen-much like her cousin Algernon-enjoys playing with fire. She continues seeing Jack even after her mother disapproves of him. She even visits him in the country and goes on her own! That is not the proper behavior of a woman of her time. Hence, Gwendolen simply represents how women can be superficial, and mischievous.