Interesting relationships/connections among population growth/migration, number of jobs created, wage growth, economic growth and comparisons among countries etc.
Macroeconomic growth models typically address growth in the environment of stationary population. Yes, we should compare growth in GDP per capita, if population changes. Migration is another story, because it is somehow different from domestic population growth. In principle, immigration would be not bad for Australia with its low population density, if immigrants would spread over the country (and not stay in large cities). About economic role of population density you can see my paper: Article Socio-economic influences of population density
I think that the article you cite has an insight: "This is more people competing for jobs and housing, pushing down wages and pushing up property prices." This means that while economy is just expanding without substantial change in unemployment rate (when the rate of job creation is about population growth). There is more demand for housing, and this benefits (rather narrow) group of developers and owners on many houses. So some rich become richer, while poor and middle class gain nothing (if not loses). I have already discussed this with you in your other question: https://www.researchgate.net/post/Do_we_have_a_relationship_between_home-ownership_among_low_income_earners_and_the_economic_growth_of_a_country
An old criterion comes to mind. I think that something must be said as to whether the countries being compared are at their full employment/full production level or what is their distance away from that level when the comparison is made. It is sometimes said that one should make sure that the countries are operating at constant returns to scale before comparing them. Also, some data providers such as GTAP and Penn World Tables make adjustments to their data base to allow comparison; it can be a monumental task to try doing such adjustments yourself.
It is very likely that the World Bank has data on average wages, GDP, population and income for several countries. I would do the comparison based on GDP per-capita. Also, IOM has information on migration for several countries.