Hi @Joshua_Dingman do you have a email domain for your “New Organisation”? if so I would probably go straight ahead and create a new organisation using that domain name. Just remember you will have to switch between organisation to keep across your different My Tasks views.
Another option would be to create a Team or Project in your personal account and then when you are ready you can move it across to you organisation, have a look at these articles;
Moving Projects Between Workspaces/Organizations
https://asana.kothar.net/
Regards
Jason.