I'd like to add to Duce's fine comments:
The cable can also be CAT 5e, CAT 6, CAT 6e, and so on, with CAT 5 being the minimum. Some cablse use the long-form label e.g. Category 5
How is the laptop connected to the internet? WWAN (Wireless WAN i.e. 3G wireless internet) or Wi-Fi? Have you used internet sharing on the laptop OS before?
I agree with Duce in preferring a router option. Another added benefit is that your A1200 can be online without the need for the laptop to be on.
When it comes to getting a power supply for an existing supply-less router it is very easy. Every piece of electrical equipment will have a label specifying Voltage (supply) measured in Volts (V) and Current (draw) measured in Amperes or Amps (A).
For example: If your router has a specification of 12V 1A, then any power supply that has a spec of 12V and 1A will work. Furthermore, the power supply can have a current rating of anything above 1A as long as the output voltage is 12V.