The AVG Toolbar does nothing to protect you, and just takes up your screen, as far as I know. Removing the toolbar might actually speed Firefox up (a little)

Do you mean AVG will still work to protect my computer and the toolbar has nothing to do with it?

Toolbar has nothing to do with it, last time I saw it. It's just web search. The only thing you should bother about is the site checker thing, but at most people common sense will work for the time being.

The toolbar adds browser-specific features.

For AVG Free 2012:

AVG Free 2012.1808 HotFix 01 adds support for Firefox 7
AVG LinkScanner 2012.1808 Hotfix 01 adds support for Firefox 7
http://free.avg.com/us-en/avg-release-notes

For AVG paid version 9:

AVG 9 is still supported for virus signatures, but I don't know whether the browser add-ons are being updated.

Hope this helps.