So back to the original OP's statement here..
VMware will not solve the IP block issue, since you're only virtualizing the internal network on a VM. This is because when you're going out to the internet, your router NATs all of your internal addresses out to a single external ip address. You can proxy the VMs by using a VPN essentially through a few 3rd party providers i've seen online.
Running VMware with multiple machines on a laptop is rubbish usually, unless you have a mobile workstation that has a nice processor and RAM, but this may be going a little too deep for most people. I wouldn't go this route just due to the sheer overhead of firing up all the VMs and VPNs to use EQ.
If you only need a laptop powerful enough to run EQ and need to mask the IPs from time to time, then I'd use a VPN service to proxy you out from your normal IP address. I would just make sure you get a good paid one, since those usually prioritize your network traffic, which makes the game more enjoyable.
As far as laptop vs. desktop, this should be always known a desktop will win every time due to modularity of the components, but laptops are purpose built with fixed hardware usually. If you need to be mobile, get a laptop, but if you don't... don't.