I grew up in Trinity Beach so am sitting tight here for nostalgia value... You can get inland in a regular car but it will be prtty damn busy: I'd say a fair chance of a traffic jam especially on the Kuranda range. One thing to consider if you are trying to get up to the tablelands is that the coastline is flat, then has a big mountain range, then drops a little and is flat on what is called the tablelands. Given that the sun will be low in the sky there is a pretty good chance that cloud build up will be sitting right at the peaks of said mountain range blocking your view from the tablelands. I'm betting on rain with a slightly better chance of seeing the sun from the coast (clouds don't bank up out on the ocean - as much) versus from the tablelands (clouds bank at the top of the range). It will be a pretty cool event in terms of darkness, birds freaking out, people freaking out either way: if we can see/photograph the sun, bonus!
Hopeful Prediction....
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Tablelands _______/\ @@@@ Clouds * Sun
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\____8_Me_~~~~~Ocean~~~~~~