I am not sure but I always up load to facebook in high quality and the pixels of my pics before upload are around 3648 x 2736. Don't know if that helps?
My friend should still need to know the final size so that she could look by herself what kind of picture she could put. So, how many pixels should it be?
My friend has also this question: if she would do a signature instead, would this be suitable size?:
It's now 796 x 146 pixels. My friend didn't put an actual picture because she wants to ask about the size first. It seems to be same sized as yours.