I am bringing some wood brackets on my luggage. Is that allowed?

You may have two problems - are you flying into a US Airport enroute to Canada? I only ask because a lot of international flights do, and then you have to contend with US Customs as well.

However, for Canada, there are certainly some restrictions on plant material, but it could depend on whether it's treated or not, wet or dry, green or not, and what type of plant/wood.

One resource for this is AIRS - the Automated Import Reference System.

CFIA-AIRS is the automated import reference system of the Canadian Food Inspection Agency (CFIA).

The purpose of the AIRS is to provide accurate and timely information on import requirements. The application uses a question and answer approach to guide the user through a series of questions about the Harmonized System (HS) Codes, origin, destination, end use and miscellaneous qualifiers of the product they wish to import.

Failing that, Environment Canada lists a bunch of species and whether or not they're allowed into the country.

If you still aren't sure, and really I'd recommend this anyway, you can contact the Border Information Service.

And finally, if in any doubt at all, DECLARE IT. If it's fine, they'll let you keep it, and if it's not fine, you won't get into trouble as you asked first.