I’d say this character doesn’t have the option to queue for the Timewalking dungeon because your iLevel is too low. Klixxy has a 103 iLevel, due to a number of low iLevel quest rewards from the Death Knight starting area that you still have on. Your Shaman is sitting at an iLevel of 109.
If you raise your iLevel by a few points you’ll likely be given the option to queue. Remember to reopen group finder after you have added a new item so it can be taken into consideration.