As a post script, you could access The End by going into Creative Mode and building an End Portal with the components available therein. I wouldn rather start a new game, since I am a Survivalist, but to each his/her own.
You only have to start a new world if you want: (1) access to The End (End Portal was added in December 19 update); (2) climbable vines (vines were added in October 16 update); (3) beaches (added today); and (4) blacksmith chests (added today).
While this doesn't apply to you, I note that if you were playing on a world created after the last major update on December 19 (TU7), then the ONLY things you would not have access to is the Blacksmith chests and beaches. Blacksmith chests are pretty useless
IMO for advanced players. And beaches don't provide any new resources or anything else of interest (they were in the game originally and were taken out in a subsequent update).