A better long term solution is to have the dynamic DNS service actually host the DNS for your domain. This will result in better performance for the users who access your site and a greatly reduced likelihood of caching problems, where a user gets a bad IP through DNS because of wrong entries still in the caches.
Setting up DNS hosting on the the DynDNS provider and telling GoDaddy that the DynDNS servers are the DNS for this domain will accomplish this.
Alternatively, the Dynamic DNS provider you reference is an ICANN registrar, so transferring the domain to them will accomplish this. I can't speak to whether they are better or worse than GoDaddy, which has devotees and people who despise them.
EDIT in response to Peter's comment/question: The DNS services are not free, but they do package deal with domain registration.