Upgrade from Magento ver. 1.3.2.4

One of our Magento installations runs on a ver. 1.3.2.4. This is becoming a problem. We need this one upgraded. This installation is running several shops and has custom themes (not advanced ones). The main webshop [login to view URL] on this installation has around 2000 products which all has several custom options. Since this is a live site, and we want every customer, every purchase etc to be included in the upgraded version - while avoiding any errors and keeping the site up live as much as possible - we would prefere to have someone make a new installation of a new magento version. Take a backup of everything from the old live site and import it to the new. And when this is done, and the theme and everything else is running correctly (we will assist to make sure this is correct), point the URL to the new installation. You must have and show that you have experience with this sort of work. Would prefere to have this job done as soon as possible since we have some new items and shops we want to add.