No you wouldn´t.

The easiest way to start to think about it is that you do not need the end question marker in this sentence as you have it in the first word.. NEREDE gidiyorsun... WHERE are you going.

Sentences with neden, niye, ne zaman, (why when what which etc) do not have MU/MI/ MUSUN etc etc (question markers )added at the end

nerede gidiyor musun?

It may be meaningful in some context.

(For example; x and y talking on the phone)

x: ...´a gidiyorum

y: öyle mi?

x: nerede gidiyorum tahmin bile edemezsin.

y: nerede gidiyor musun?

x: evet bir balonda ...´a doğru gidiyorum.

thank you insallah. Thats makes it clearer for me.

Balonda gitmek de mümkündür, ama seyahatin çok uzun süremez...ancak balonun bir köşesinden diğer köşesine gidebilirsin.

Eğer niyetin balonu bir vasıta olarak kullanıp, mesela A şehrinden B şehrine, gittiğini anlatmaksa iş değişir; "balonda" gidiyorum değil, "Balon ile gidiyorum" demek gerekir.

It may be possible in my Turkish. We speak different languages, I guess.

We can try the same thing in English as well.

I ask their opinions from English speakers here:

I´m going by balloon. (sounds weird to me)
I´m going in a hot air balloon.
I´m going on a balloon. (could be right, but I wouldn´t use it..)

I´m going by taxi.
I´m going in a taxi.
I´m going on a taxi. (wrong unless you mean you´re on the roof)

I´m going by submarine.
I´m going in a submarine.
I´m going on a submarine. (this one could be okay, just like "on a boat," or "on a plane," but I wouldn´t use it)

I dont understand now, why it´s nereDE gidiyorsun and not nereYE.
I thought in Turkish it must be like that,which is unlike in my and English language.

"nerede gidiyorsun" and "nereye gidiyorsun" don´t have same meaning.

"nereye gidiyorsun" means "where do you go?"

For "nerede" lets imagine a dialogue like this: 

A: Üniversiteye gidiyorum. 

B: Nerede gidiyorsun?

A: Ankara´da.

In this dialogue "nerede" has a meaning like "in which city"

Sagol gokuyum.