Are there only sons of perdition and no daughters of perdition? Please let me know!
The 76th section of the Doctrine and Covenants, verses 31 and 35 detail what it takes to become a Son of Perdition.
31 Thus saith the Lord concerning all those who know my power, and have been made partakers thereof, and suffered themselves through the power of the devil to be overcome, and to deny the truth and defy my power
35 Having denied the Holy Spirit after having received it, and having denied the Only Begotten Son of the Father, having crucified him unto themselves and put him to an open shame.
Please note that the kind of open rebellion that this is talking about isn’t done by accident or through ignorance. It is willful and deliberate turning your back to the Savior as you see him standing there.
As for the gender issue. Typically the male gender is used as a default when both male and female are meant. I suspect this is the case here and I see nothing in the requirements for this great fall that would exclude it from being able to happen to females as well.