As far as I understood you are looking a custom page in Q2A to display probably external content on it and set it as homepage on q2a site. Or you want to create a custom page in q2a for some purpose programmatically not through Admin > Pages to display any logical or custom content on that page.
If I am correct and you have any of the above scenario, you can make a custom page module in the plugin and set the request part for your page.
Then you can directly access your page via URL and no need to create any page in Admin area. I am using this technique in my upcoming plugin.
I have created Gist for you. This is a kind of boilerplate and you can straightly use to create your plugin.
Let me know how is that for you!
Q2A Market Gist