There's no Django way™ of displaying math equations. There's an HTML and JS way though. And you will be forced to do some of the work by hand.
As you can see in these SO questions from 2008 and 2010, the best way to embed latex equations in a webpage seems to be MathJax (used by math.stackexchange.com), the replacement and evolution of jsMath by the same developers. Read the MathJax documentation to get a hang of it.
The complex part is that you want the output panel to be dynamic. I never used math.stackexchange.com myself, but you could try to mimic what they do. Or just call MathJax after each keystroke if it's not too heavy.