With a new domain name, simply put, you may need to start over with the search engine ranking process, as rankings are associated with a domain name in combination with the actual code/html/content of the website. Depending on the domain name and how it has affected your rankings thus far, will depend on how it affects you after changing it.
While your existing content should help, you will need to re-establish your inbound links to the new site and re-build up the page rank. In addition new domain names can take up to 6 months to be considered permanent and get better ranking.
No matter what, changing your domain name will affect your search engine rankings, largely because each search engine responds differently to such changes, but you can substantially limit the damage done.
One method which can help search engines know about your change, is by using 301 redirects. At your request, LinkUSystems can easily redirect one root url to another root url using a HTTP 301 (permanent) redirect.
You can let Google know about a domain name change via Google's Webmaster Tools. See more information here: https://support.google.com/webmasters/answer/83106?hl=en