All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is permissible for a woman and others (i.e. men) who are not obliged to perform the Jumu'ah (Friday) prayer to offer the Thuhr prayer before the Friday prayer (is prayed) after making sure that its time has started. Ibn Qudaamah said:
"As for those who do not have to perform the Jumu'ah prayer, such as travelers, ... women, ill people, and all those who are excused, then they may pray the Thuhr prayer before the Imaam performs the (Jumu'ah) prayer according to the view of most scholars.” [End of quote]
Based on the above, it is permissible for you to pray the Thuhr prayer on Friday after ascertaining that its time has started, even if this is before the end of the Friday prayer [in the mosque].
Allah Knows best.