Welcome to the forum and also indeed welcome to Australia. It is so very difficult moving to a new place let alone a new country, we moved to Thailand to live for 6 years so I totally understand trying to integrate into a whole new way of life. It is so great that you have found your way here for some support and some comfort in what is a very concerning time for you as a parent.
It is great that the hypnotherapist was able to help your daughter with the crying but I think she might need another level of support, like seeing a doctor, general practitioner. She may also benefit from talking to someone like a counsellor, the school that she is attending might have someone that you can get to chat to your daughter to help her settle into this really distressing time for her.
It is hard being a young adult, let alone moving to another country and trying to manage it all and fitting in. That is great that she has expressed what her fear is, you can perhaps help her with this by reassuring her that you are not going anywhere and you are right here with her.
It is so wonderful you have reached out here to get some support, there is also a service available called Kids Helpline on 1800 55 1800, they deal with people under 25 for support and it would be great if you could suggest a call to them to your daughter, or even if you called to get some tips and then perhaps even get her to speak to them with you.
You are doing a wonderful job, it is not easy being a parent. Hugs to you.
Hope to chat soon