Looks like you got the easy project. The other student in your class had to design and build a car cheaper, more reliable and more fuel efficient than a Toyota Camry in one week.
Gas chromatographs are highly engineered pieces of equipment that have evolved over 50+ years. Every part has a history of engineering to it. There was a review article a few years back in "Trends in Analytical Chemistry" called The History of Gas Chromatography describing the advances to the columns, detectors etc.
Here is what I would do. Buy some Swagelok fittings to connect to your nitrogen line (I would use nitrogen as the eluent - not methane), a gas regulator and a pressure gauge in the 1-100 psi range. Buy some semi flexible steel or aluminum tubing of the same dimensions as the Swagelok fittings. Find an old oven that you can drill into the side of. Pack some diatomateous earth loosely (pressure drop should not be greater than 30 %) into the tube and then coil it neatly. Run the sides of the tube in and out of the oven and seal the vacant space with an insulator to prevent heat loss. Where the nitrogen comes from, connect a "T" tube with one side going to the tube in the oven, the other to the nitrogen source and the third to a septum (a piece of rubber) that will seal the gas in but allow your test mixture to be introduced via syringe into the flowing nitrogen. Split the tube coming out of the oven into a T also and run the tubing into two separate solutions.
Here's the tricky part. Try to find two organic chemicals of moderate to low volatility that will give a visible chemical reaction in the solution (ie color change, precipitation, heat with a thermometer in the solution etc) The differential in time between the appearance of the visible reaction will represent the retardation factor related to either separation or volatility. In reality, most GC's use polydimethylsiloxane (a viscous goo) lined on the walls of a highly coiled glass capillary column and the separation is due to boling point / volatility variations more so than adsorption.
THe variables would be
1. Pressure of the flow gas (observable by regulator - faster should cause material to come out faster)
2. Temperature of the oven (higher = faster).
3. Create another column of longer / shorter length or different packing material
It should qualitatively give a student an understanding of the variables affecting hold time in the column.