Welcome To AA!!! This is the one that doen't
tell you not to drink before talking to us. But it probably helps.
Back to your question, your filter does not need an air pump to operate. It is a power filter. This means it hangs on the tank, sucks water up the long tube, forces it through the filter media and it flows back into the tank. The water impellor and the motor that drives it are in the filter. If that was more info than you needed, sorry. I tend to lecture.
Anyway. power filters work very well on smaller tanks. I'm guessing this is a 10 gallon kit?
If you wish to, you can get a small air pump to power an airstone for a bit more water circulation, or to run one of those cute decorations with the bubbles and moving parts. Many are a bit tacky, but some are kinda neat.
Good luck with the new setup, any questions or problems, give someone a holler.
P.S. If you go to the articles section on the home page here you will find a number of good articles to help you get atarted. In particular the one on a fishless cycle will be of great help!!!!!!