A trick which might help in future:

You don't actually need to write the tune out again to transpose it
For a tune written in E (or Eb) you just play every note as if it is written ONE LINE (or one space) above where it is actually written.
(using the NEW key signature of course)

Then you will play automatically Eb as if it is G, and all the other notes will be correctly transposed as well.

(Physically, you could draw another line on the staff, through all the Middle C's, so they become E's, and tippex out the top (F) line, if that helps the illusion)