There is still no definitive answer for this. The government shutdown delayed the regulatory process, but you can read here that SW has completed its first test flight to Hawaii. It is very likely that we will see an announcement for when the flights will launch very soon, but that is just my opinion. Keep in mind that another possible shutdown could further delay the approval process.
Feel free to Google Southwest Air Hawaii to read all the press coverage and speculation. You can also find SW's official Hawaii page here.
-A List, Companion Pass holder
