I doubt this will work as you're expecting. There's an easier approach.
IP addresses are part of "networks" (and smaller "networks" are called "subnetworks", a.k.a. "subnets"). They are frequently grouped geographically.
The IP address given to you by GoDaddy is likely pointing to their network. By saying that the IP address is yours, I believe they mean that the address can be used to point to equipment on GoDaddy's network, and that equipment will serve your websites. There will not be any other customers who have websites use the same IP address that is reserved for your stuff. So, in that sense, it is yours.
What I presume you want to do is to host a web server at home. If you want an IP address to point to your equipment at home, get such an IP address from your local ISP.
GoDaddy's services can still be useful for DNS. You can have a domain name registered from them, and use GoDaddy's web interface to make that domain name use DNS nameservers that reside at your house.
Whether your laptop gets the IP address that your ISP provides, or not, depends on your connection type. This can be done with "bridging" setup. In other cases, your "modem" ("DSL modem"/"cable modem") is what gets the IP address, and your internal equipment get private IP address. However, that's okay, because you can have your modem use "port forwarding" to send the HTTP traffic to your laptop. Your laptop can then respond to the traffic, so from the world's point of view, the HTTP traffic does appear to be coming from the IP address, and the HTTP content is being provided by your laptop.