I'm not specifically familiar with Vonage but I believe it's much like Skype. I assume this is a VoIP phone combined with a service from Vonage. The VoIP 'phone will need internet access (broadband) to work and then I assume you'll need to check if the existing Vonage service is available at your new location (it may be limited to a specific IP address). If not maybe you could use your VoIP 'phone on Skype?
What you can try is connecting the unit (to your broadband router) when you arrive in Antigua and seeing if it works (which it may well do), if not, move to Skype (but see below before you do this!).
I also believe that there are, in theory, restrictions in the use of Skype (and similar) in Antigua due to telephony monopolies on the island. These are licencing issues not technical issues. Maybe somebody could confirm the current situation for you.
Anton & Tracey