Is there enough depth of water to take a vessel with 2.2mtr draft inside of Curtis Island?
I did it in a cat , 3 feet draft but 20 feet between hull centres. My observation was plenty of depth but stick to logical channel. I touched once but on a rising tide and no problem , Lucas sets out a good plan for using the tides and good waiting areas close to each end of the cattle crossing.
Coast guard Gladstone will give you good advise. If I remember correctly you need your draft plus 1.2m to calculate the height of tide you need to cross the Narrows. In your case you will need a 3.4mt tide. A Gladstone local May want to correct me on the 1.2mt. I draw 2.1mt and I came round the outside as the day tides did not work for me.
I have done the Great Sandy Straits with a 2.2 m draught and that was fun but as for the Narrows, the question is why would you do it???
It is sand fly paradise (if you are a sand fly and hell if you are human), what with waiting for tides etc, the outside passage will take less time, it will be motoring most of the way and if you miscalculate the tides and ground, you could be stuck there for a month or more. It is not terribly scenic either.
If you want to do it for the navigational challenge, go for it.
The outside waters offer a good passage with a couple of interesting anchorages which I have done a few times.
The inside passage with a 2.2 m draught is pushing the limits, particularly if it is a fin keeler. A fin keeler will hang up with 2 inches less water than it's draught and be almost impossible to reverse off.
Qualifier:- I have never done the Narrows. 
You are welcome. Enjoy your passage.
However, do not let my advice stop you from turning south once you have passed the top end of Curtis Island. What is called the Yellow Patch is a very popular stop off and there is Hummocky Island a few miles north east of the top end of Curtis which has a good anchorage for a S/E blow.
If you want to cruise this bit of coast between Bundaberg and Mackay, get ahold of Noel Patrick's "Cruising the Curtis Coast". An excellent guide because he was a local ( was as in passed away but his children have updated and kept his legacy alive) and is somewhat regarded as a legend.
If you are sailing over from the west to do the east coast of Aus, I believe the Queensland coast will somewhat blow your mind.
There ain't no other place like it on Earth.
i really enjoyed the outside route for Curtis.
also really enjoyed pancake creek to the south for drift diving and fishing.
Probably irrelevant and too late now, but,
we did the narrows in November with 1.7m. That was the maiden voyage after her 10 year rest.
Caught the morning tide through and headed to Sea Hill for an overnighter before heading to rocky.
Did pass one poor unfortunate soul who had landed himself up in the mangroves, but we had an uneventful trip.
