I had my first at 35, my second at 37, then had two miscarriages (the second being twins), and then my third child at 40. I'm going to start trying for number 4 soon. My doctor did loads of tests and it turns out I have a gene mutation called PAI 1. It causes blood clots in your uterus and I guess can lay dormant and present itself randomly. I had no problems with my first two pregnancies. I injected Lovenox with the third child and carried him to term no problems. I will have to do the same with the next.
Did your doctor tell you that you had to go through genetic testing? I wouldn't think it would be necessary. I refused any of that. THey asked if I wanted it because of my age and the increased risk of abnormalities, but I told them I only wanted tests for problems that could be solved in the womb...like heart defects. If any other abnormalities showed up like Down Syndrome, I would still carry the child to term and love it like any other. Aborting a child because of physical issues is not an option for me. So unless that is an option for you I wouldn't think they would do any of those tests without your permission.
And they can't stop a miscarriage due to chromosomal problems if I'm not mistaken...so what's the point.
There is a very large population of women having babies in their 40's now. Look into the statistics and see what you find.