Very interesting question. I think you would benefit from looking at 3 particular aspects of female characters in this play to help you answer this question: the friendships that women have between themselves, the character of Hermia and the character of Hippolyta.
The relationships women have in this play deserve close examination, for in some cases they are shown to be superior to the relationships female characters have with male characters, and in some cases they are shown to be destroyed by petty rivalries and jealousies in the course of love. Interestingly, the first type is shown by Titania and her justification for keeping the Indian changeling boy. She tells Oberon in vivid terms about her relationship with the boy's mother:
In the spiced Indian air by night
Full often hath she gossiped by my side
It is for her sake that Titania will not abandon the boy. This relationship then seems to be more important and more tenuous than the relationship between Titania and Oberon herself, and arguably it could be this that drives Oberon to jealousy.
You can see the second type of relationship between Hermia and Helena - Helena, distracted by her unrequited love for Demetrius, betrays her dear friend and her plans to elope with Lysander, in the vague hope that it will make Demetrius like her. Later on, both of them, faced with Demetrius and Lysander loving Helen, fight and exchange viscious insults. Female friendship in this instance is something that seems to be easily broken and rather fragile.
The character of Hermia, especially in Act I Scene 1 is worthy of attention, as she is very bold in defying her father's will - in spite of his rights by the law - and refusing to marry Demetrius. Women of this time, we are told, were literally regarded as their father's possession, fit to bestow who they thought appropriate, and Hermia's actions show her to be a woman of considerable pluck.
Lastly, you will want to examine the character of Hippolyta. Interestingly, directors have differed in their casting of Hippolyta, some of them showing her to be happy with her lot and in love with Theseus, others showing her to be a conquered bride - forced into marriage with Theseus, and therefore creating an interesting parallel with the situation of Hermia and Lysander. The recent(ish) film with Sophie Marceaux playing Hippolyta depicted this very well, with Hippolyta obviously identifying these parallels and unhappy with Theseus for not doing anything about it, but in the end loving him for letting the four lovers marry. If you look at Hippolyta's speech, especially her first speech, where she does not seem to be as enthusiastic as Theseus to get married, you can easily see this perspective.