There are many, MANY christians who do not believe in young earth creationism. Your religion may be a leap of faith, but it is not necessary to extend that faith until it contradicts known scientific fact (age of the earth, evolution, etc.). In addition, the Vatican has recognized evolution as having merit, and it has been my personal experience that most christians do accept the scientific fact of evolution and an Earth that is several billion years old.
In addition, the bible does not explicitly state anywhere that the Earth is 6000 years ago and that every creature on Earth was created just as it is now and has not changed at all. That interpretation is actually somewhat new (well, a few hundred years old) and is based on some highly questionable math involving the number of generations it lists from Adam and Eve until Jesus.
So as a quick answer, no, you most certainly do not, and you will find a great deal of company with fellow christians if you choose to acknowledge the scientific fact of evolution, and an old Earth.