All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm in praying while having one's hair tied according to the described manner stated in the question if all the hair and body of the woman is covered except her hands and face. Tying one's hair in a given manner has nothing to do with the validity of the prayer. So your prayer is correct, Inshaa' Allaah. Please refer to Fataawa: 82912 and 83482 regarding the required clothing of a woman in prayer.
Allaah knows best.