The statement "emotionally unstable" is very broad, and so it could be difficult to say whether it needs to be disclosed prior to a marriage proposal or not.
If she has a chronic illness that would affect her spousal relationship, and impede in what people would see to be a healthy marriage, then it is best for her to be upfront about everything so she is not left with a broken heart or an early divorce.
In general, it is always better to be direct and clear about one's mental state of being, and to mention what would be for or against them.
Everyone is entitled to get married, even if they have certain challenges they are facing, and of course she can get married if she is emotionally unstable, but honesty is always going to work to everyone's advantage.
Hopefully, with therapy and support of her family and loved ones she can overcome these emotional difficulties, and maybe marriage will secure her mental stability, in shaa Allah.
With prayers for your success.