Brick up on top of dwarf wall

First thing I'd inspect is the quality of the foundation, most dwarf walls aren't built on substantial foundations. The foundations may not take the extra weight of a full height wall.

Save yourself the expense,if its a privacy matter just put Satan glass in or panels that suit

I would suggest a trial dig to check foundation depth before adding any extra weight with additional brickwork. There are other alternatives on market sips panels or Ultraframes Hups walls which are a more lightweight option ..

Dwarf walls usually have dwarf foundations. 600mm is standard but my structural engineer has specified in past 400mm on a single story cavity wall. So with that in mind I would ADVICE (not specify)400mm. Dig down and inspect. Employ a structural engineer for professional advice. Option it to use thermal block and tank outer skin.

All footing are built on the earth and most are concrete foundations but if you go back several centuries houses were built on soil with no concrete foundation at all just a pyramid type structure footing