A few weeks ago it took me 75 minutes to get from Poipu to Tunnels Beach, without any delays due to traffic. That's probably not too much different from the drive you are talking about, since the added time to get from Princeville to Tunnels on my drive would be about the same as the added time to get to Port Allen vs. Poipu on your route.
So, as I mentioned before 1-1/2 hours absolute minimum and I concur with those recommending at least 2 hours. Unless you opt to plan this as an overall south shore day trip, you will want to take the Kapa'a Bypass and after you go past Kauai Beach Villas don't turn right toward Lihue but continue straight, past the airport and Nawilwili, reconnecting with the main highway near the Kukui Grove shopping area.