Iron levels

I am recently diagnosed (last month) and have been reading up on pd as you might imagine. I have read that we have iron deposits in our brains when these are analysed after death.
Do others have higher iron levels in their blood tests? I am interested in this because I have coeliac disease and have been on a wheat/gluten free diet for years - one of the key elements of this is to keep my iron levels up. My GP took blood tests before I was referred and commented on how good my iron blood count was for someone with coeliac. Is it common to have higher iron levels in blood tests?