Sentences 1 and 2 sound more natural than sentences 3 and 4. But all four of them need to be modified to sound correct and even more natural:
1. As I watched The Lion King on TV, I got an overwhelming urge to travel to Africa / to go to Africa.
2. As I watched The Lion King on TV, I took it into my head to drop everything and go to Africa / and travel to Africa.
Sentences 3 and 4 can also be made more natural by once again changing "go traveling" to either 'to travel to Africa' or 'go to Africa'.
In this context, 'go traveling' doesn't sound natural to a native ear.
You could use it if you changed the phrasing:
One day I would like to go traveling *through* Africa.
To go traveling *around* Africa is a dream of mine.
But in general, this structure 'go traveling' doesn't feel right if you use it with the preposition 'to' after it, as in your four original sentences.
I hope this helps.