I would definitely suggest a stronger reed. You can get some high notes out with a strength 2 reed but they probably won't sound too good and you will squeak a lot. I would suggest at least a 2 and a half but eventually you will have to go to a strength 3 reed to really get a good sound out of the high notes.

High notes require a lot of air from the stomach so just make sure you support those notes. Try to tighten up your lips when you play a high note so you don't squeak/go flat. Make sure you constantly keep your instrument warm as you practice so your notes don't sound dry or airy.