If you get a barrel you'll be able to assemble the gun with it yourself, but it may be unsafe. You need the headspace checked, at least, and that may reveal the need for some fitting. Shotgun frames can't take rifle barrels, rifle frames can take shotgun barrels. Details on the H&R website should enable you to figure it out, but basically, your .223 rifle frame should be able to take any other centrefire rifle barrels. E.g. my .223 Superlight has a .308 barrel, too.
However, that's moot if you can't get a barrel. Even in the U.S., H&R doesn't sell spare barrels because of the potential liability issues if they are fitted by an owner or an incompetent gunsmith. You send the gun to them and they fit the additional barrels you want. Unfortunately, they only do this for customers in the continental U.S. The extra paperwork for import/export isn't worth their while.
Workaround 1. Get one of the site sponsor dealers here who do imports, e.g. Questar, Prophet River, to get a U.S. dealer to send a Handi-Rifle to H&R to have all the barrels you may ever want fitted, then import it.
Workaround 2. Get lucky on the EE like I did. I don't know why some gunnut had a couple of spare barrels available a while ago, but he did, and I bought the .308 for my .223 Superlight, and it just happened to fit well enough.
Workaround 3. Write to the Gravel Agency (google will find them for you.) They are the Customer Service Agency in Canada for Remington, Marlin, H&R and they would like to import barrels and run the Barrel Accessory Program for Canada like H&R does in the U.S. The more of us who indicate we will be customers, the better their chances of persuading H&R to let them try this.