No, engine failures are not related to "Ageing Aircraft".
Almost all of the rotating parts in the engine, plus a lot of the stationary parts (eg, Nozzle Guide Vanes) are "consumable" parts, in that they will eventually wear out and can't be repaired, or will be automatically replaced when they reach their service life limit (e.g Turbine discs).
What that means is that even though in theory an engine may be "twenty years old" most of the critical parts will be no more than four or five years old.
Furthermore, in order to balance out engine shop workloads, it was common practice years ago to take one or more of the brand new engines off a brand new aircraft and fit an older one, or parts of an older one, so as to "average out" the age of the engine pool. Don't know if Qantas does it that way. But if they still do, your "New" Aircraft won't necessarily have "New" engines at all.
As for working out if QF is having more or less engine failures, I would assume that QF keep failures /by type/by module/by engine hours/by cycles data and probably time/temperature/pressure/rpm history as well. It's very simple to apply a Poisson statistical distribution to the data and set confidence limits that will tell you if something really has changed, or if all you are seeing is a set of coincidences.
Not that QF would tell anyone if there was a real change for the worse...