I don't think it is a fair comparison. The cost of raising a child can still be too high even in a fairly low gini country.

In fact I'd say gini has nothing to do with birth rate. Birth rate declines when parents have confidence that there is a good likelihood their children will survive to adulthood.

It is often easy to forget that just five hundred years ago almost one of two infants born didn't survive into adulthood. Low birth rates are good. Don't let anyone say otherwise.