Blossom, if the GP refers you, won't Flinders then do it? I expect they just don't do the nt scan routinely not that they won't do it at all.
I looked up some research on the topic and there doesn't seem to be any evidence for first trimester scan being better or worse than 18-20 weeks, except of course in putting the mum's mind at rest. It seems a few abnormalities can go undetected on the earlier scans, but not significantly. Perhaps this is why they wait.
Why don't you just get the referral from your GP?