You can cycle a 2.5 gallon tank (actually I'm in the process of doing this right now).
You have the Red Sea filter right? I don't know about these but in the filters I use I haven't had to replace the media yet (in almost 4 mos).. even though its says replace monthly on the package its better to just wait until the cartridge starts falling apart.
The bacteria will grow on whatever is in the filter. But your main source of bacteria will be in the gravel/substrate, decorations/plants, and wall of your tank... not the filter itself. When you replace the filter media just cut a piece of the old and put it in with the new so the bacteria can recolonize quickly.. then remove the old piece and discard.
Anytime you change anything in the tank (take out gravel or decorations, change filter media, do big water changes, etc) you want to test your water for a few days after that.. you may go through a "mini-cycle" as the bacteria recolonizes. Its nothing to worry about but you want to make sure your prams don't go too outside the normal limits. Of course if you get readings of ammonia or nitrite after replacing your media do a small water change.