My wife was in nursing school all of 2019 except for June through August. However, each semester that she took was 11 credits. Would this qualify as a full time student?

It should--but you can ask the school what they consider to be "full-time."  Why are you asking---toward what deduction or goal?

The only thing full time (FT) student status would affect would be the dependent care credit. Then she gets an "allowance" for the earned income limit while a FT student. 

Most schools require 12 hours for FT.  But, as xmasbaby0 said, you'll have to check with her school.