Private vs public doesn't impact the speed at which the results are composed, as all results (in Vic) are done at the one place. First trimester screening requires a private Ob or a GP to fill in the paperwork so it is kinda always done privately (in that public hospitals don't organise it).

I had similar issues with delays and was also p1ssed off. I believe it is due to GPs not knowing, or being too lazy, to follow up the results soon after the scan. If the blood test is performed a week before the scan, and the sonographers send the results to GHSV (or the appropriate State clinic), you should have the results within a day or two of the scan.

However, it is good that they let you know that both your measurements look good so far. Hope they don't take long for the risk figures.