Measure combining growth and distribution of income A frequently used measure of economic progress is GDP growth. (There are alternative economic indicators as well, such as the Human Development Index.) But there are problems with GDP growth. For example population growth also causes the GDP to grow, because more people produce and consume more goods. You could correct for this by usind GDP/capita growth instead. 

But GDP/capita growth still does not take into account the distribution of wealth. Perhaps 90% of the population are doing worse than last year but 10% are doing so much better that on average there is still growth. You could argue that this is still 'better' overall, but I would argue that in a democratic setting most people would probably not vote for an economic policy that clearly and openly supports such an income shift. (If you are thinking of cases where this has happened and will happen: I am afraid I don't care about the political side of this argument. You are welcome to post about it over at politics SE.)

Are there indicators that capture both distribution and growth of income?
 A simple example with its own faults would be median GDP/capita growth. Something better (and slightly more complicated) could probably be constructed using the GINI index.
 Alternatively: Are there arguments against measuring something other than aggregate or average GDP?
One concept fairly established in economics is the idea of generalized Lorenz dominance.

The Lorenz curve (https://en.wikipedia.org/wiki/Lorenz_curve) plots percentiles of the population on the x axis and the cumulative percentiles of income on the Y axis. If the point (30,10) is on the curve, then this means that the bottom 30% of the population have 10% of the income of the population.

This allows us to compare the inequality of two countries by comparing how low or high their Lorenz curve is. If curve A is everywhere above or equal to curve B, then A is weakly less unequal than B. However, even the poorest person in B may still earn more than A.

The generalized curve multiplies the Y axis with the average income of society. Now we can not only compare A and B in terms of inequality, but also by how well individuals are off in these societies. Curve A being everywhere above or equal to curve B means that every percentile of society A is weakly better off than every matching percentile in society B.

Shorrocks showed that under certain conditions a parameterized family of social welfare functions is higher in society A relative to society B for all parameters if and only if the generalized Lorenz curve of A is higher than B at all points.

Shorrocks, Anthony F. "Ranking income distributions." Economica (1983): 3-17.