Gerbils are great pets but do better in pairs of at least two of the same sex. Keeping one alone can cause it to be lonely even if you do spend a lot of time with them. Also, they are up at all hours of the day, active during the day and at night. They also need special care, you will need to either get a pure metal cage (no plastic at all on it) because gerbils will chew out of a plastic cage, or a 10 gallon aquarium (minimum). If you put them in an aquarium you will need a fitted lid because they can jump out if given the opportunity. Also, they will need a wheel, and since they chew so much it would need to be a metal wheel.
Not only are gerbils very active but they chew... a lot! I have to constantly buy new chew toys for my gerbil because he will chew through every new toy I get him in a matter of a few days. Also, gerbils dont like to sit still, most gerbils when held do not stay in one place because they basicly have better things to do, places to go, people to see, things to chew.
If that sounds like the right pet for you, then go for it. Otherwise if you want a more calm pet try a hamster since they can be kept on their own.
As to how to convince your dad, simply show him that you are responsible enough. Do chores around the house to save money to buy everything that you need. Keep your room clean, do the dishes. Also, do research, find as much information as possible and read it all, then present it to your father in an educated manner. Tell him about their personality, how it will show you how to be more responsible, how they are great pets, their cost, etc.