KesTag

I don't understand the above statement, I'm from Melbourne and I think someone is pulling your leg (probably someone from Sydney ? ). Shops are open Tuesday in Melbourne  - even the Victoria Market opens on a Tuesday (closed Mon&Wed).   It's the second (or could be the first now) largest city in Australia. It's a very beautiful city with wonderful architecture, great shopping district, and considered Australia's culture, food and cafe capital. Adelaide is a lovely city - the city of churches. Sydney is in a beautiful location.
Also - South Island New Zealand is on the cool side, even though it is the middle of summer (roughly 18C/64F). 

Another option is to call Royal Caribbean and have them setup MTD reservations for you at the times you want each night.  Also let them know the size table you want if you want your family to not be stuck with other people.  Then check and make sure the reservations show up in your calendar.

You can reserve times for MTD from your Calendar in the Planner.  MTD is classified as an activity.
Click on My Calendar, the click "Add Activity", select Dining, select your day.  When the dining activities pop up, find My Time Dining then add it to your cart.  At that point, you can select the passengers and you'll be presented with a list of possible times.  You'll eventually check out and you're all set.

Our experience has been consistent with what @DMLM reported.  We use a travel agent, who typically follows-up with Royal to get us a seating in traditional dining after we've been defaulted to My Time.  I also agree with @FManke , and have used that strategy after we checked in Day 1 (before Cruise Planner was created).

DMLM has it correct.  OP currently has "My Time" dining and is on the waitlist for early seating.

There are two main dining room times (early & late seating).  If you were confirmed in one of the spaces I believe you would just see the time next to dining on your booking.  When you see MyTime it reflects that you are not confirmed at either early or late seating and have the flexibility for your MyTime dining.  The (Waitlist) I believe is indicating you are looking for early seating in the main dining room or that is the time you are looking for MyTime dining.
I took a look back at a couple of my last bookings (within the year) as I was not 100% sure.  I saw the waitlist timing before I was confirmed with the time I requested (as we prefer a structured time).  When I was confirmed I did not see MyTime or (waitlist) times reflected and just the time.
 
I hope this is correct for you.  You can always call your travel agent and have them try to confirm timing.  If you booked directly with royal you can do that with them also.  I will tell you that I have booked many cruises directly with royal, have Diamond + status now, and have had to wait for confirmation so it does not always happen the first time :-)
Good luck and enjoy your first trip!
 
D 

It showed up in my Jan 2020 today