I am currently using Quickbooks Desktop Premier NonProfit Version, and I would like to switch to Quickbooks Online. Because of the two different versions, will that be a difficult conversion?

Go to menu File > Utilities > Copy Company File for QuickBooks Online. If you are using QB Desktop 2016 or older, you may open your data file on trial license of QB 2020 Pro to minimize any problem.

https://quickbooks.intuit.com/learn-support/en-us/new-subscriptions/download-a-trial-of-quickbooks-d...

Once you are ready to proceed, open a QBO account with the current discounted plan. You may get a discounted price for up to 6 months. 

https:// quickbooks.grsm.io/US

https:// quickbooks.grsm.io/us-promo

As the final step, check your converted data in QBO

https://quickbooks.intuit.com/learn-support/en-us/set-up-payroll/what-to-do-after-converting-from-qu...

Short answer is yes.  Not everything is transferred, see this

https://community.intuit.com/questions/1145236

a non partisan comparison of QBO vs QB desktop 
http://onsale-apparel.com/Rustler/qbo-or-qbdt 
(cost comparisons are at the end of the article)