Hmmm, Firstly, we would be asking why your current host believes you should move to a dedicated server. In our experience a very small minority of clients genuinely need a dedi.
We do offer dedicated servers and if you are positive that is what you need we will supply, just open a ticket to pre-sales.
Managing a dedi is not for the inexperienced user.
We have found that there are hosting companies that will entice clients to them with incredibly low cost hosting accounts, with all the bells and whistles that they tell you you must have - unlimited this, that and the other! Within a few months they will suspend your account for actually starting to use the 'unlimited' resources and insist you move to a dedicated server - which of course they will sell you ;-)
If the above sounds familiar, hold off from the dedicated server and speak to someone in our hosting department who can advise on the best solution for you based on your server statistics.
You really should never outgrow a hosting company, they should be able to allow you to grow and develop your business with support and guidance. We certainly will!