Yes that is what we are doing too. I am just going to the passport office to do the second passport. Will be doing that the second I get home. Very close to our office. You have to send in your original passport when you apply for the second passport as well. So I need my passport back for Inca.

The second passports are good for four years. They have a different passport number.
Critical any paperwork accompanying the trip all uses the passport number you are planning on using. A mismatch could be a problem.