Yes, more convicts were sent to Australia, but we also had more non convicts come out in that timeframe, so we ended up with fewer convicts per head over that period. They were also mainly indentured here, and spread out. Only those seen as criminal were kept in prison camps - I suspect the same happened there. And Canada was seen as wilderness, as there were very few people there, they were constantly fighting wars with the French, so extremely few North American convicts went to Canada. So much so, that after the war of independence, Britain had nowhere to send convicts so they started to invade Australia. And, of course, the Canadians were fighting not to become part of the US, so sending convicts there wouldn’t have been a good idea.
Immigration from other countries wasn’t very limited, especially once the gold rushes happened in Australia. Most Australian colonies didn’t have convicts when they were founded. Some decided to get convicts because they were growing very slowly and they needed more people, especially as the French were seen as a threat. There were convict outposts that didn’t last more than a few years in some places, but they were gone before the colony was founded - for instance, there was one near Melbourne in 1812, but it only lasted a few years. It was long gone by the time the colony of Victoria was founded in 1838, and by 1849 Victoria was big enough to be gazetted as a separate colony. Then the gold rushes started in 1850, and Victoria quickly became the largest colony, with ships pouring in from all over the world, including from the USA, since the California gold rushes were slightly earlier. The Scottish highland clearances and the Irish potato famine brought a lot of British immigrants.