You're right, it can be made to a verb with する.
Your first sentence sounds fine, but the second is slightly off. Just swap the places of へ and に and that should be it. So it would be この週末にリオデジャネイロへ旅行する。
Personally, I prefer using 旅行に行く and 今週末, though. I'd say 今週末はリオデジャネイロへ旅行に行く. Google seems to agree with me because this kind of sentences come up with much more hits than "旅行する" used in a similar way.
I've learned Japanese mostly by speaking though so you might want to wait until someone comes and explains you the precise grammatical rules using all the fancy grammatical terms, though, since I'm quite oblivious to those.