You'll need to install Reason on both computers (which is allowed). The only thing you can transport from one computer to another is your files: songs, patches, refills, patches.
You can download the reason install exe and put that on your external drive so that you have what's needed to install reason on any computer you want to use - this is what you'd do if the other computer is not connected to the internet. (make sure you download the 3GB+ version that includes the Factory Sound Bank and Orkester).
HP Pavillion DV7T-3300 Laptop | i7 Q720 @ 1.6 GHz | 4GB RAM | Win7 Pro 64-bit
m-audio Axiom Pro 61 keyboard controller || iPad2 | RetouchControl DUO | TouchOSC | LoopBe30 MIDI
m-audio Mobile Pre USB (original) audio interface | ASIO4ALL || RØDE NT-3 mic
Reason 6.5.3 || Pulsar | Saturation Knob | Rough Rider | TSAR-1 | Uhbik-A | Re-Tron | Polar | Echobode | Uhbik Q | Uhbik F | Morfin XF | Uhbik S | Uhbik D | Uhbik G | CV Suite Line Processor | wbl5515 | Uhbik P | RE-2A | Radical Piano