The lady in question is Katarina Gustavsdotter Vasa, Princess of Sweden. She was born in 1539, married Edzard of Ostfriesland in 1559 and died 1610. She was quite well educated and seems to have excelled in theology. She seems to have been a smart woman, having an influence both politically and religiously.
I find this portrait a bit odd. There is very little information about it and the date online is 1750! It certainly doesn't look like an 18th century painting, though it might be a copy from that time of an older painting. It is known that she was painted in 1556 when she was 17 and this may very well be it. I am certainly no expert on 16th century fashion, especially not German fashion, which seem to have influenced Sweden the most, but most German gowns I have seen from this period doesn't looks like this.
It is, however, her loopsided headband that I think looks really strange. Have you ever seen anything like it? Her hair seems to be scraped back into a decoarted cap, and then this jewelled band. My first thought was that it may hide a scar or birth mark, but a painter could easily paint that out. On the other hand, if she did have a mark of some kind, then perhaps it was her "thing" to wear something over it and it became part of her person style. Regardless, I think it is an unusual portrait. What do you say?