(You don't even have to own the new domain for this to work, you could set up redirects to someone else's site if you wanted to)
In terms of Google, will they be keeping the old domain up there along with the new domain as well for a long time? Is it possible that I will lose all of my SE rankings and have to start over? And will I need to time this domain launch along with Google's quarterly 3 month deep crawl or can I do this at any time? Keep in mind that we do not want to be penalized for duplicate content on Google for both domains, at all if possible. We are looking to keep our rankings intact but for the new domain. Maybe we don't need to do anything at all except for the .htaccess redirect and Google will just know that the new site does not get penalized for duplicate content?
One quick word on this too: we will be keeping the old domain and have it redirect to the new domain forever. Will the old domain eventually be removed from Google completely as soon as they see the redirect taking place?
If you can afford to, it's a good idea to keep the old domain there with the redirects active forever. Although search engines will, in time, update their indexes and remove the old site, there could well be people who have linked to your old site or bookmarked your old site, and the chances of getting all these people to update their links and bookmarks is small.
If you put a redirect in place and the new website is clearly an evolution of the old one (bearing in mind that Google focuses on content rather than visuals), you shouldn't lose your rankings. You might experience a temporary dip while Google works out what's going on, but once it's done that it should put you back to where you were. It certainly shouldn't take 3 months, at least not to get the main pages done (although some deeper links may take longer to be crawled and updated), I would have said that a few weeks should normally be more than enough. (On the other hand, if it takes longer then it isn't the end of the world, because the redirects will ensure that everyone is taken to the right page even if they follow a link to the old URL)
A useful tip is to use a canonical tag on every page. Add a line like
<link rel="canonical" href="http://example.com/page/">
to the <head> of each page, giving the URL that you want to be indexed for that page. Combined with the redirects, that will help Google to understand that it is not duplicate content, it is the same content but at a new URL, so it will transfer the rankings and link juice more quickly.