Get yourself the WikiCamps app if you haven't already. It will be your friend!
Plenty of the truck stops that do allow free/low cost camping will allow you to use showers, either for free or by donation/small fee. Just head in and ask when you pull up (as some places that used to offer free camping and are on WikiCamps may not still be doing so). From memory we stayed at the Charters Towers Puma servo in 2016 (not an awesome spot to camp - its at the back of the truck parking area, minimal space, plenty of dust, traffic and truck noise) and were able to use their showers.
Also, PUB CAMPING. Free or low cost camps, access to toilets, showers, cold drinks, hot meals... Now, that's a pretty awesome way to travel! When we did the Cape and were around the Nth QLD area we stayed at the Ashton Hotel and the General Gordon Hotel and LOVED them as low-cost camps. Both had showers we had the use of and decent meals. Pretty sure the Ashton Hotel has been sold since we were there (had been on the market for a while when we were chatting to the publican back in 2016), but I think they are still offering camping. Apparently there's a Facebook group dedicated to pubs that offer camping... was told this by a publican on the weekend at a pub we stayed at near Toowoomba (Aubigny Hotel). I wouldn't know as I'm not on Facebook! LOL! She was saying that pubs across the country that offer camping advertise on there. But we've found all the pubs we've stayed at via WikiCamps.
Also, there are coin-operated showers in some towns. Usually roughly $2 for a 3min hot shower where they are offered. Not always near campgrounds, sometimes in pretty random council parks/etc. Check out POI's on WikiCamps to find these, or use filters to search for showers.