According to the very interesting Australian publication 'Plants of the Merri Merri' (1) the "tubers" of Eleocharis acuta are edible "raw, baked or ground into flour" which would be quite exciting as the well known related Water Chestnut (Eleocharis dulcis) is an edible tuber. But I can't find anything about this plant having tubers edible or otherwise, instead it only seems to have a creeping rhizome which I believe I have photographed the white tip of above.
My guess is this report, intended for the general reader not botanists, refers to this white rhizome tip which I find edible, the white part is soft without fibers, easily eaten. It tastes bland, starchy and innocuous, without the crunch or flavor of Water Chestnut. Tim Low reports "Aborigines ate the starch in the young underground stems" (2) of the closely related Eleocharis sphacelata, this sounds like the same thing since a rhizome is a modified underground stem (3), I've not tried or examined Eleocharis sphacelata.
The rhizome tips I found were small and fairly sparse, they hardly seem worth it unless you have a lot of plants and time to harvest them, though the plant is particularly pleasing visually. I tried a New Zealand native of this plant, it is possible the rhizome is bigger in Australia but reports seem to be about the same, 1-2 mm in New Zealand ,1-3 mm in Australia. E sphacelata rhizomes sound more promising 10-15 cm, though I can't find any first-hand accounts of eating them.
Both Eleocharis acuta and Eleocharis sphacelata are native to New Zealand as well as Australia, but do not seem to have ever been reported as being eaten here in New Zealand.
(1) Plants of the Merri Merri. A Home Gardener's Guide to using Indigenous Plants in the Northern Suburbs of Melbourne. Editor Rebecca Wigney 1994
(2) Wild Foods Plants of Australia. Tim Low. 1988.
(3) https://en.wikipedia.org/wiki/Rhizome
