Your ticketed points remain the same (you're not changing a transit to a stopover or v.v are you?), so the $125 fee is not chargeable
And since you are in business class, no service fee is chargeable (per the Qantas web page)
So definitely HUACA, and have the two snippets of rules ready to quote to the CSR.

FWIW, I have ticketed with QF in the past, and never had a problem changing dates for no charge.

I have purchased an ex-CAI DONE4, starting next month. In due course I will need to change dates (dates towards the end of my itinerary are dummy dates). So I'm interested in the outcome here.

A final ploy might be to mention the "A triple C" (Australian Competition and Consumer Commission). The ACCC has recently fined Qantas for selling tickets for non-existent flights; so mention of the ACCC might trigger some positive action.