Certainly looks like a funnelweb (a female), but I doubt it is Atrax robustus, which is not recorded south of Kiama and Gerringong (see Michael Gray's 2010 taxonomic revision of funnelweb spiders, downloadable from https://journals.australianmuseum.net.au/gray-2010-rec-aust-mus-623-285392/). It is more likely to be the so-called Blue Mountains funnelweb, Hadronyche versuta, which Gray records from many Illawarra, Nowra and Jervis Bay localities.
Having said that, this is still one to avoid! Especially the males, which are the deadly ones. I seem to recall that a woman was killed by a funnelweb at Currarong, before the antivenom was available.