You can do it using just Dojo Base — no need to include anything, if you use the trunk or Dojo 1.3:

dojo.create(div, {id: div1_1}, div1);

This line creates a div with id div1_1 and appends it to the element with id div1. Obviously you can add more attributes and styles in one go — read all about it in the documentation for dojo.create().