Doing it fast and successfully
Theoretically with a 301 redirect for the whole site to a new domain, your new site should gain all value that the old site had achieved, at least over time. However, practically it can be different.
There are two elements to a transfer to a new domain that might come into play:
1. A 301 redirect tells the search engines that the old URLs are no longer value -- everything should be transfered to the new URLs. The old URLs are removed from the index, the new URLs are indexed and will take the place of the old URLs with regard to most SEO factors. However, not all search engines are fast enough to do the transfer without a short break. It is also possible that the old URLs are removed before the new ones are actually indexed. For this reason it makes sense to promote the new domain name before adding the 301 redirect - work on getting the new domain name (with the existing site) indexed as much as possible before using the redirect to transfer the rest of the value to the new domain name.
2. Your homepage generally has the highest value, meaning it will get crawled more frequently. Let us assume you have a redirect on the whole site. The redirect will be found first on the root page and most likely processed first. The new URL on the new domain has only links to the new domain. The new detail pages are found to be duplicates of the old detail pages and perhaps filtered from the search results. This can lead to the old pages remaining in the index, but not crawled (because of the lost value through missing links) and the redirect not found for some time.
If you can get the full site indexed at the new domain name before the redirect, you should be fairly well off. Better would be - though technically harder to manage - to redirect the detail pages first, wait a while, and consecutively move to the higher levels until you redirect the root page last.
So - in short, from best to pretty good to worst:
1. index the new site, redirect detail pages first
2. index the new site, redirect everything
3. redirect everything
4. just remove the old site and hope Google finds the new one