Dating

Should I ask her out?

I moved away for uni last week and met a girl who is in a course group chat with me. We have talked on there for over a month and she mentioned on the group chat a few days ago that she had been feeling really homesick (she has travelled from abroad alone to be here) so I messaged her asking if she wanted to meet and perhaps do some shopping or go for a walk to help her get her bearings.

She said she would like to and so I met her, her roommate and another girl on my course a few days ago. We talked briefly in public and then decided to meet later in the evening after we had gone home and had some dinner. Later at dark, I met her and her roommate in a park, we sat and talked for a while and then took a walk.

Yesterday we met again and went for coffee and to do some shopping and then I walked her home. Over the last few days we have been messaging privately a lot and I think I am starting to develop feelings for her. However, I am reluctant to ask her on a date in case she says no and it ruins the friendship. Given the limited info I have provided, what do you think I should do?

Thank you for the advice in advance, please vote and comment!

P. S. This is not something I am planning on doing immediately, however advice would still be appreciated!
Ask her out
Remain friends
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