First of all, let me commend you for your desire to learn your religion and practice it better. I pray to Allah to help us all to remain steadfast on it.
Now coming directly to your quesiton, I wish to state the following:
Prayer in congregation is more rewarding than praying individually; since there is no mention anywhere in the sources that the rewards thus promised apply to men only, there is no reason to exclude women.
Based on this, you should pray in jama'ah whenever you are together. There is no reason for you to do it on Fridays only. The mothers of the faithful such as 'Aishah and Umm Salmah set the precedents for us; they are certainly our role models in such critical issues affecting women. They should know better than men, as their knowledge is gained directly from the Prophet (peace be upon him).
For further details, please consult the following answer.