If you already had a trial account with Qualtrics, or have an account from another institution, it is not possible to directly collaborate across these accounts. Collaboration only works within the scope of the school license. However, there is an easy option for transferring the survey itself (the data is a separate issues). Qualtrics allows an easy export and import mechanism using .qsf files.
When you have your survey open in the source account, use the advanced menu at the top right of the screen and select export survey. This creates a .qsf file of the survey which contains all the information about the blocks, questions etc. needed to reproduce the survey in the new location. When you log into your new account, create an empty survey and then use the same menu to select import survey. You will then have an empty copy of the survey to work with in the new account.