Hi,
I think this would be relatively easy to add and would make using WebIRC better. It's a feature that Slack has and it is convenient, because it allows using more of the UI without taking hands off your keyboard (they're commonly there due to the chat-oriented nature of the app).
Alt+Up Arrow = Go to Previous (one higher) channel/pane.
Alt+Down Arrow = Go to Next (one lower) channel/pane.
Hard Mode
If you want to really to go all out, you can also implement 2 more shortcuts:
Alt+Shift+Up Arrow = Go to Previous channel/page with unread/new messages, if any.
Alt+Shift+Down Arrow = Go to Next channel/page with unread/new messages, if any.
I use these shortcuts in Slack quite often because they are useful. :)
See its keyboard help for reference:

Thanks for making an awesome persistent web IRC client!
Notes
Alt and Option are the same key.