Here is how you can fix it:
If I could outrun my body, I
want towould fly to all the mountains on theEarth; I want towould fly to the Moon, to theMars, to thePluto...
Could and would are parallel verb forms.
In English, we say "the moon" because Earth has only one and it doesn't have a special name, but we don't say "the" with most proper names, including when we use the word Earth to mean the name of the planet.
The semi-colon is needed because you are beginning a new independent clause with "I would..."; however, if you want to leave the comma as a matter of personal style, I won't argue!
Student or Learner