Yes, it's grammatically correct. The difference is that it focuses on telling the listener where you see a beautiful tree. Duo's suggested translation above focuses on telling the listener what you see outside. Look right before the verb in the following question and answer pairs:

Mit látsz kint? Egy szép fát látok kint. (What? A beautiful tree.)

as opposed to

Hol látsz egy szép fát? Kint látok egy szép fát. (Where? Outside.)

Yes, you can say it but then the emphasis of the sentence will change. The word before the verb is emphasized.

Én egy szép fát látok kint. = I see a beautiful tree outiside, and not a bush.

Én kint látok egy szép fát. = I see a beautiful tree outside, and not inside.