Your description is a bit confusing... What object are you referring to when you say "sprite"? With animation, do you mean a special "fire" effect or just the laser shot moving? Maybe a simple sketch could illustrate the problem...
In general, I would approach the problem as follows: store an STL container for the laser shots currently in flight. These can be sprites for simplicity, later you'll want to separate graphics and game logic. Then, when the player fires, you add a new shot to the container; when it leaves the screen, you remove it.
If you're not familiar with the STL, take a break and learn it carefully, because it's an absolutely crucial tool in C++ that will accompany you every day.
By the way, please use [code=cpp] [/code] tags for code