I think it depends on where you live. I live in Canada and if you are "late 30s" they will test for several things after only a few months of trying. They will test your FSH to see if you still have plenty of eggs, they will test your partners sperm for quality and quantity, they will also test a big range of other stuff such as thyroid, blood disorders, lupis.
I would go to the Dr asap and ask for all the tests they can give you - if you have a challenge ahead of you, you might as well find out early.
Good luck!
Pea