MacOS – OSX ML Terminal – Switching tabs

If you're serious about terminal work, I would suggest looking at tmux, especially as new builds of iTerm 2 come with it precompiled in (though I use the 'vanilla' version). In your case, if you were using tmux you could detach the current session from the window you're in, and then reattach in a new one (i.e., full screen), or just have multiple windows attached to the same session. There are some other advantages to using tmux, but I'm sure you'll discover them as you're using the program more.

Alternatively, have iTerm show the tab bar even if you only have one tab (make sure Appearance > Hide tab bar… is unchecked), and then you can 'pull' the tab out into its own window to continue using it.

It is possible in nightly release of the alternative terminal program iTerm2 via Preferences → Advanced → Tabs: New tabs are added at the end, not next to current tab set to No.