Hi @Julie_Hasler 
Thank you for reaching out!
As it stands, it is not possible to move Forms between Projects.
There is an existing thread in the #productfeedback category requesting the option to Save Forms as Templates: Can the FORM in Asana become template or Save as a template? - #11 by Aline_Bergamo
I’ve you haven’t yet, I would recommend you to add your vote and comment to it!
Please, let me know if there is anything else I can help you with! Have a great Wednesday!