Your impulse is very workable. You will need to install a vapor barrier that comes with the laminate. This is both a cushoin and a barrier. There are many manufacturers with different systems. Most are the click-and-go style that do not require glue or nails.
You will need a quality power miter saw, mallets and the ability to read instructions.
You biggest difficult will be removing the existing baseboard and replacing it after the laminate in installed. Also, the transition at the doorway(s) will be tricky. There are specialized transition strips which would normally require nailing . . . you will not be nailing into the travertine. You will probably be using the strongest construction adhesive (PL Premium) you can find to glue the transition to the laminate at the doorway(s). You may also have to cut the bottoms of the doors if the added elevation from the laminate makes them impossible to swing.
There are many DIY sites with advice on installation. Here is one that is helpful to the first-timer: