Dear sister,
As-salamu alaykum
Given the inherent flexibility in the prayer routine, it is a matter of choice given the situation whether the hair is covered or not. The main directive for both genders is implicitly good, wholesome, modest adornment or attire (7:31).
However, if you are praying in a congregation or amongst those that feel head covering is mandatory during prayer whether religious or as modest attire, I personally find there is absolutely no wisdom by causing undue disharmony, rancour or to upset the congregation.
We are encouraged to assimilate
[1], especially during prayer; to come to common terms, arguably in the widest sense possible.
For example, when I am amongst a Sunni congregation (regardless of what madhab), I pray like the congregation in situ. If I am amongst the Shi'a, I pray with their routine. I have even prayed to God with the People of the Book who I find closely represent truth. My purpose is to pray to God, worship Him with all my heart and not to cause undue hardship for others or become a source of agitation for them.
I humbly believe that is the beauty inherent in the Quran-centric approach. It is an 'encompassing' approach and allows inherent flexibility. I believe that too, to be a Divine blessing.
I hope that helps, God willing,
Joseph
REFERENCE:[1] THE IMPORTANCE OF CONGREGATIONAL PRAYERhttp://quransmessage.com/articles/congregational%20prayer%20FM3.htm