In any relationship going slow seems in my sight to be advisable. Finding common ground is a good basis for a relationship. Finding out if the friend likes you as a friend or likes you romantically may take time to fathom out.

Is this her first relationship with the same sex? If so another reason to go slow. This is not a direct to romance situation.

I am not an expert, but if you are full of anxiety, that is a third reason to slow things down. Take some months to get to know each other as people. If you have a therapist talk to them about your anxiety. Sometimes that is the tip of the iceberg that keeps us from having deep meaningful relationships.

Do you feel a relief? That is the sign that things are going slow enough. If anxiety peeks out again, slow down.