@Clare *********
I believe they say 10 working days. You'd want to check the website of the Thai embassy or consulate you'll be using, since there are 2 in Vietnam. I'd apply sooner rather than later.
Take note as this is very important. If you are going to be applying for a DTV for one of you through taking a course, and the other will be getting a dependent DTV visa, you will have to double the time. The first person must apply, wait, and RECEIVE the DTV visa first. And then the 2nd person can apply after the first one is received. That's because one of the required documents in order to apply for the dependent DTV is a copy of the primary person's already issued DTV visa.