Is Fajr prayer considered void if performed with the intention of timely performance while having misgivings about whether it is a timely or a make-up prayer?

The time for Fajr ends at sunrise. Whoever catches one or two rak'ahs before sunrise, their prayer is considered adaa' (performed on time).

The questioner's prayer is not invalidated by her doubt as to whether her prayer was adaa' or qadaa' (performed as a make-up); for it is not a condition for the validity of the prayer to have the intention of adaa' or qadaa'. The most beneficial cure for waswas (obsessive whispering) is to disregard it.