Have you been charting BBTs to confirm ovulation each cycle and to check that your timing is good?

I agree with myturn that, after 2 years, you are well and truly entitled to a referral to a fertility specialist. In fact, you can seek a referral after only 12 months (and only 6 months if you're 35+). Heck, I was offered a referral after only 8 months when we were TTC#1 (I was 31 at the time). You need a referral for the specialist's fees to be eligible for medicare.

There's a lot of testing that a specialist can do and their labs are generally better-equipped for fertility testing since that's all they do. There's a lot of different test that can be run depending on where you are in your cycle and what information your Dr wants.

If you wanted to do some preliminary testing before seeing a specialist, I'd probably just suggest a progesterone test to confirm ovulation. It would need to be done at 7dpo (or approx 7 days before AF is due, assuming you have a 14 day luteal phase). I've always had to pay for those sorts of blood tests though when I've requested them through my GP and they're not cheap. Charting BBTs can generally give you the same answer, but for the cost of a thermometer (about $20) - it just takes longer.