Dog fighting, as in two planes shooting at each other?
The players plane could move using arrows or wasd, let it move freely all over the screen.
An enemy plane would chase the player;
chaseTime = distance between the two planes / players max speed.
heading = a point that is the players speed * chaseTime added to the enemy planes x/y position.
And then the enemy plane should ease to the heading point.
Then you would create a pool of bullets, you don't need much, and use that pool for shooting and displaying bullets,
each bullet being marked either a player bullet or enemy bullet and collisions being handled that way, but both player and enemy reloading from the same bullet pool, it is a efficient way of handling bullets.