How to measure quality of education across countries?
A good reference is the Barro-Lee Dataset wich gives educational attainment
for 146 countries from 1960 to 2010. The data are disaggregated by sex and by 5-year age intervals. Their estimates of educational attainment provide a reasonable proxy for the stock of human capital.

An older reference is hosted by the World Bank.

In case you need more recent data, you may apply their methodology.