Classes can have static methods. Static methods do not need a class instance to be called for.
Timer1 timer = new Timer1();
By default, the Arduino does not implement the new operator. Even if it did, the new operator returns a pointer. You are not trying to store the pointer in a pointer variable.
it said: "Timer1 does not name a type"
Have you looked at the source code? The class is called TimerOne. The header file declares an instance of that class called Timer1.
It is that instance of the class that you are using, whether you are aware of it, or not.
What does the rest of your code look like? How is the switch you are using wired?