Welcome to the Bunnings Workshop community @hec5. It's fantastic that you've joined us and many thanks for your question.
I believe the best way to rid your lawn of this grass would be targeted poisoning. I'd suggest the use of a Yates Zero Weeding Herbicide Applicator Brush filled with Zero super concentrate. The wand has a brush on the end, which dispenses the poison. Simply walk around, painting the tips of the unwanted grass. The poison will kill the grass and leave the rest of your lawn untouched.
Once the grass has been removed, you should find these step-by-step guides useful in restoring your lawn: