I think that "go" is not necessary since you don't say that you are going to a special place. Unless you use it in the continuous form meaning future (I'm going to reap...)
Also, even if the original holds the structure as you translated it, in English the statement would read better:
"I'm going to reap cherries this summer"
in the Romanian text, "mă duc" means "I go", and I think the meaning is actually that I go to a special place...
I think "I'm going to reap" has mostly the meaning of "I will reap", which is not the same...
Still, you are right about the adverb's position, so maybe it should be "I will go to reap cherries this summer"
Just wondered whether here by "reap" you mean "pick".
To reap means to gather a crop by cutting. So cereals (wheat, corn, barley...) are reaped. In the gathering of cherries, it would be more than unlikely that the cherry trees be felled (chopped down) in order to do so
Here the word the most usually used would be "pick" => I will go cherry picking this summer.