You also sound very similar to me - we were TTC for just 4 months before I consulted my GP, as I had (correctly) suspected for a number of years that I had PCOS due to highly irregular and missing periods. I don't think that you are jumping the gun if you already suspect that you are not ovulating - it is a very different scenario from somebody who has a very regular cycle as it is really hard (if not impossible) to identify your fertile periods.
You will probably be sent for blood tests in the first instance and if they suggest PCOS, an ultrasound to try to confirm visually. My ultrasound appointment took nearly 6 months to come through, by which time I was already booked in for a Laparoscopy (camera through a keyhole incisiion under GA). My initial consultation at the local hospital took 3 months alone to come through, so I was very pleased that I had approached my GP when I did.
If it is PCOS, it is likely that you will be prescribed Clomid in the first instance and you will have blood tests to see if you ovulate as a result. You may also be prescribed Metformin, which is a diabetes drug, to try to control blood sugars and address the resulting hormone inbalance.
I turned out to be resistant to Clomid, so was twice given Ovarian Drilling (under General Anaesthetic), which can help to improve PCOS, but unfortunately to no avail.
We finally came to the end of the road with the NHS after about 20 months, as they weren't able to offer IUI / IVF, but I must stress that this was before the "free IVF for all" rules came in. We went for IUI privately, waited around 3 weeks for a consultation and happily I conceived DD 2 months later after just 2 cycles.
I would try to get your investigations done on the NHS if you can wait, as these usually happen quite quickly but if the conclusion is that you need IUI / IVF, and the waiting times are long, then you are in the lucky position of being able to go private, which will of course get you seen so much quicker.
Like the other ladies have said though, IUI / IVF is not an inevitable route for PCOS sufferers, some people conceive naturally and others respond really well to Clomid. Good luck!