Mykonos side trip from Naxos

Both are possible, it all depends on what you want to do/see. Know that if you take an organized tour to visit Delos from Naxos, you will spend a few hours in Naxos.

Several agencies in Naxos offer tours, see for example Zas Travel
https://zastours.com/

or Naxos Tour

http://naxostours.net/en/naxos-tours-greece/

To go to Naxos by yourself by ferry you can look for the timetable on ferryhopper

https://www.ferryhopper.com/en/#/

Choose the Island hopping tab (not the single trip) and enter Naxos as departure, Mykonos as destination 1 and Naxos as destination 2.

Then select the same date for trip 1 and 2

No need to book in advance, buy your tickets on the day of departure at a ticket sales office

JoLui, thanks so much for the sharing of your knowledge. I have been able to plan my trip using a lot of your advice!