It is safe to can the soup in quart jars.  There are specific instructions for how to can soups so they are safe.  They need to be processed in a pressure canner.  Don't add thickeners such as flour, rice, noodles, and specific instructions if you add dried beans and legumes.  You can read all about it in the following handout https://extension.oregonstate.edu/sites/default/files/documents/10396/sp50931soups.pdf.  
If you have other food preservation questions you might like to call the OSU Food Preservation Hotline open M-F from 9 am-4pm.  Certified Master Food Preservers are available to personally answer your questions. <personal data hidden>.  

Good luck canning soup and Thanks for using Ask Extension.

Nellie Oehler