-Yes, your kid can apply for the OPT after she has been F1 student for one year. She does not need to have a job first to a apply for OPT, but the OPT will be counted after it is approved no matter whether she has job or not later.
I still also think your kid can be qualified for the CPT because 做與專業有關的校外暑期工作 cab be counted as "Internship". So, she may just talk to her professor or academic advisor about this and then, her professor/advisor can add this校外暑期工作 as the professional training Internship. Many students do that.