Shalom R' Aaron!

Great to hear from you.

Excellent question! It seems that Rashi (29a DH Ihi) addresses this important issue. Rashi tells us that from the words "Bechor Banecha" alone, we would only be able establish that a father does not have to redeem his daughter. Theoretically, however, as you noted, there may still exist an obligation upon the daughter to redeem herself. The rationale for this would be two-fold. First, the Mitzvah of Pidyon is not considered bound by time, and therefore women ought to be Chayav. And secondly, the interpretation of the word "Tifdeh" as "Tipadeh", indicates that not only the father has an obligation to redeem his children, but also that the children -- after they grow older -- bear the responsibility to arrange their own Pidyon. Therefore, it is necessary to learn the daughter's exemption based on the rule "Kol she'Acherim Metzuvim Lif'Doso" etc.

Warmest regards,

Yishai Rasowsky