I recently changed domain name of one of my sites. I changed ip address for that domain in my godaddy account. It takes sometime about 24 to 48 hours for dns propagation. That means your website might not be available around the world during that time. You might want to wait during that time before redirecting your old domain to new domain.
There are tools for checking website availability. They can check status of your website from different servers.
I found below sites useful for checking dns propagation status
1. Site24x7 website availability checker
Site24x7 tool allows you to check your website from multiple locations. You can check your site from 32 locations worldwide. I use their website monitoring tools for one of sites. It works good. They have other free tools like dns lookup, ping test, trace route etc. i found this site to be most useful.
2. Whats my DNS
Whatsmydns allows to check your dns from 16 locations. It shows all these locations on a google map. this is useful for visualing results
3. ViewDNS – DNS Propagation Checker
ViewDNS checks status from 19 locations around the world.
4. Preshweb dns checker
Preshweb dns status checker is an open source tool. You can query a random list of dns servers. It has about 61 servers in its list. My query resulted in testing 10 servers out of 61 servers.