I suggest a cautious approach.
Laser hair removal is very safe in general. However, there is a small risk of triggering an acute flare of eczema. It is good that your daughter has not had any recurrence for 5 years, which means that she is at a lower chance of an eczema flare.
I suggest that you try laser hair removal with a doctor who is confident of managing eczema. In the rare event that it happens, a range of topical steroids creams and oral steroids are required.
Hope that this helps!
Warmest regards,
Dr Justin Boey