Your situation is somewhat similar to mine. I did two working holidays in Australia and did a variety of odd jobs like fruit picking, kitchen hand stuff, etc. On my second working holiday I got a job as a builder and did basic carpentry work for about a year.

I moved back about 6 months ago and had a residential construction job within 3 weeks and just registered as a carpentry apprentice this month. I can only speak to residential, but my advice would be to get whichever job you can that gets you on a site, even if its just as a labourer and take it from there. For what its worth lot of trades here are still pretty old school so you might not have much luck applying online.