So what shouldn't be there? Well, most of it. You don't need a whole section of "Advantages over other frameworks" and then a table comparing to other frameworks.
You don't need most of the overview you have. Just picking something random: there's a full table with methods of Q.event. These are details; it's simply too much information that is not helpful to someone who wants a general overview of your project. The same can be said for most of the stuff there. The section on templates is useless for a README: It shows some very specific details (like the fact that there's a Q.Template.load.options.dir) without actually showing a real-world example, because foo, bar, baz, Some/name, and the code actually shown is all synthetic and abstract.
And that's the other problem: It's generic info. And so we get to what the README is missing: A simple, complete, minimal, working example.
And, yes, you end up the README with "Putting it all together", I know. But again, it's an abstract and generic thing. It shows a bunch of code ideas just thrown together for the shake of showing them. Even the comments in that code say things like "you could do this", "you could do that". It doesn't really help.
What you really need is something like a counter and two buttons to increment/decrement, or an input box and a list that gets filtered as you type, or whatever. Something silly and small... but complete and working. You don't need to show off all the features in that example. Just make sure that the code in the example clearly represents the typical way you'd write it and that you can hopefully keep it under 20-25 lines. Make it so simple and self-explanatory that you don't need to add many comments or any at all if possible. Ideally, make it so that you can actually just put that code into CodePen/JSFiddle/JSBin/CodeSandbox/Plunker/WhateverYouPrefer and then link it with "See this example live".
Again, it won't show all the features available and that is fine. But it will give the reader a fairly good idea of the general approach and the feel of using your framework. Because right now, with so much information the README gives a feeling that your framework it's anything but small, that is something complex with lots of abstract options and ways of doing things.