I enjoyed reading this. I wonder how much of your daughter’s hesitation is also the stigma that women can't do STEM related jobs or tasks.
Girls have it much harder because (a) there is a drive in our culture to tell girls that they are pretty or beautiful regardless of their physical appearance or characteristics and (b) engineers are commonly considered to be nerds or geeks, not that there is anything wrong with that.
There is a lot of research related to STEM and the gender gap. Verizon posted a video and a blog article last year. In the video they said that 66% of 4th grade girls say that they like science and math but only 18% of all college engineering majors are female.
It could also be that she does not want to be her own boss. There is nothing wrong with that either. Not everyone is a leader.