If you look at the same data release, the excess deaths are almost entirely in cancer and dementia in old people (with the exception of a spike in diabetes at the same time as the spike in COVID infections likely due to it being a significant comorbidity).
So whilst I m sure the higher excess deaths in Australia is difficult to explain (as there is probably a multitude of factors). The theory that somehow the vaccines give people dementia or cancer (which have not been associated with COVID or the vaccine) AND these usually relatively long term diseases go on to kill them within a 2-4 month period AND this only happens to old people for some reason AND other countries have not observed a similar pattern despite the vast number of vaccines given, seems highly unlikely.
In addition, assuming the author is referring to the UK ONS, our public health body does release excess mortality estimates on a weekly basis - and unsurprisingly they correlate with the waves of COVID infections, not the vaccination program.
https://app.powerbi.com/view?r=eyJrIjoiYmUwNmFhMjYtNGZhYS00N...