What causes curding in this case: heating milk with large quantities of sugar
It's not the sugar that caused the milk to curdle, it's the milk itself. Dulce de leche and caramel are both usually made with either cream, condensed, or evaporated milk. The issue with regular milk (especially skim), is that it has such a high water content and low fat content. The fat in cream buffers the protein, helping to prevent curdling, and the canned milks have already had most of the water removed, making them less likely to curdle. 

The sugar could also have a buffering effect on the milk protein, unfortunately you have a catch 22. In order to buffer the milk form curdling, the sugar would have to be dissolved in the milk. In order to dissolve sugar in the milk at a 1:1 ratio, the milk would have to be heated past the point where it would curdle.

You might be able to prevent this by using a double boiler until the milk has reduced a lot. Making a caramel requires almost all of the water to be cooked out of your syrup, so this will take a really long time and isn't advisable.