I have a bit of sympathy for that. I HATE needles, even the sight of them turns my stomach. However, I had to inject our sheep last week.
I just got on with it, and it went ok of course, but it's ok for your granddaughter to be a bit reluctant!
That said, when my Sister (now a vet) was still at school, she did as much work experience as she could with local farms, vets and even an abbatoir. That did her no harm at all when she finally applied for University - they could see that she was serious, and it helped her to get a place (difficult, when good school grades are a prerequisite rather than a selection factor).