eTA is already issued to you if you have WP of any kind. I've got email from IRCC few months ago about that.I'll copy paste it for you.
Also ,i suggest you to stay here until you resolve your status. I went to Europe last summer and i had horrible experience on Dublin International airport.Flight companies sometimes are worse than immigration officers and you need to show everything you've got when it comes to immigration papers and if he doesn't believe you ,he won't let you board the plane.I'm from visa exempt country and EU like you and there's no way that i'm going home ever again until i finish this immigration process.
A message from Immigration, Refugees and Citizenship Canada
Beginning March 15, 2016, visa-exempt foreign nationals will require an Electronic Travel Authorization (eTA) to fly to Canada. U.S. citizens are exempt from the eTA requirement.
If your study or work permit was issued on or before July 31, 2015, you will need to apply for an eTA if you wish to enter or return to Canada by air on or after March 15, 2016.
If you received your study or work permit on or after August 1, 2015, you were automatically issued an eTA with your study or work permit.
For more information, and to apply for an eTA, please visit Canada.ca/eTA.
Thank you,
Immigration, Refugees and Citizenship Canada