Then after about six months - put some actual content on the dot.com. You will then have the chance of taking over 2 slots in the serps because the dot com will have authority and some remaining backlinks out there.
The advice I've most often read is to (slowly) 301 permanent redirect old site/pages to new site/pages, keeping an eye on the new site's performance. (I'm not 100% certain that "slow redirecting" is universal advice.)
Since it's a charity you might have some success asking inbound linkers to point their links to the new site/pages.
Finally, I'm not sure if there's (an effective) way throught G's webmaster tools to "tell G" about the move.
Any other ideas/suggestions?
[edited by: Webwork at 2:51 pm (utc) on Sep 7, 2010]