@Pablo74 There is a markdown-it-mathjax, unfortunate for you, they do not provide a UMD version of it. So, you will not be able to extend the UMD version of QMarkdown with it.
Create your own component wrapping QDialog (with all the things you need, as you need them, including how content is injected or used) and use that component wherever you need it with the components option of Vue. https://012.vuejs.org/api/options.html#components