This message is based our my wife and my recent experience (February, 2018) in driving between El Calafate and Puerto Natales. It partially is based on the difficulty we had in obtaining accurate information. Overall, one should not be discouraged from doing this trip by oneself. It is not difficult. It is safe and the roads are, relatively speaking, decent.
You need only two types of documents. The first is a passport. The second is a car permit which allows you to leave Argentina and enter Chile and then do the reverse on coming back to Argentina. We got this document from our car rental company for a $ 90.00 fee. You must show the document on leaving and entering each country where it is signed by each respective border guard. I do not know if the document is available elsewhere, such as an online web site. This was the most expeditious thing for us to obtain it.It also must be returned to the car company upon returning the car to Calafate.
Routing and border crossing:
We entered Chile at the Rio Rubio/ Dorothea crossing. Rio Rubio is on the Argentine side. You then drive about 10 km to Dorthea on the Chilean side. Getting to this crossing takes a little longer than some others. However, we were advised to do this as we were told the traffic and time taken at this border is quicker than other crossings.
Leaving Argentina and entering Chile took together maybe 20 minuets. The only minor hold up is that in entering Chile you must take all luggage from your car into the customs building and have it scanned and inspected by the Chilean custom officials. There are no other departure or entry fees.
On our return to Argentina, we had a slightly longer time entering Argentina as a tourist bus preceded us. However this only took about 40 minuets total.
I think time can alter significantly because of how busy these stations are, and particularly whether you get behind tourists buses. However, we were advised that fewer buses use this border crossing than some others.
Road conditions and routing:
We drove from El Calafate to Esperanza, Argentina and then Esperanza to Rio Rubio. This is not the fastest way to go. However, all roads are paved. There is relatively little traffic. The condition of the two lane highway, except about 50 km before Rio Rubio is good. Those 50 km can have some large potholes—-but no worse than some roads in Pittsburgh in the winter time!
The drive is rather scenic. The total drive took us under 5 hours including border crossing. It can be very windy on the road.
If you fill up your car before leaving El Calafate, you will not need gas until you get to Puerto Natales. There is a gas station before Esperanza and at Rio Rubio. There are no tolls on any of the roads.
Make sure you drive toward Esperanza before going to Rio Rubio. There as a turn off way before Esperanza which will indicate a road to Rio Rubio. Do not take this road as it is a dirt road. About three km before Esperanza you will see signs to Rio Rubio.
There is no reason not to do this ride. We are 75 year old travelers and did not have any problems. If you are staying in Torres del Pennes, the National Park in Chile, the ride will take about another hour longer depending on what entry you use to get into the park. Many of the roads within the park are dirt roads. However all roads from Argentina to the park are paved and in decent condition.