Only if you're not already on a 'new' server (in other words, all the Aussie servers) - you have to pay to move from one 'new' server to another, which, kind of makes sense, given that is a carrot to try and lure people on congested servers to new ones (a friend of mine wanting to move back to the US servers found this out the hard way today).

So unfortunately if you're already on a new server like the Materia servers, if you want to move to the Dynamis server group you'll have to pay for the transfer alas.