I don't want to fall into the trap of mind reading
I do it all the time but I call it 'advanced empathy'. I get enough 'hits' to make it worthwhile and I'm careful about how I phrase it (a diffident "I'm wondering whether..." or "I have a hunch that...") so I'm ready to hear I've got it wrong.
I think that she needs a steady relationship/life partner.
I'm not comfortable with that as a primary need. Good relationships don't fill a yawning chasm, they work best when people are already sorted. Maybe she would be happier if a prospective partner took an interest, but that would prevent her working on the real issue. If she feels unloved, that's worth exploring further.
... give her the certainty that what she needs will come along at some point and she doesn't have to worry about this for now, just concentrate on her studies etc and just 'live in the moment'.
That sounds good.
I may have to include something that says 'you know what you want so go out & get it'..
That puts back the pressure you just alleviated!
Do you not have regular supervision to discuss this kind of thing? It's mandatory for therapists in the UK and Australia.