I feel for your daughter. Clothing tags and seams can be very uncomfortable
and itchy! Especially now that many garments are made with nylon thread!
Ouch! 
I might recommend satin bias binding be sewn over the seams of her current uniform. Being bias, it has plenty of give - but I agree with nylkaenid, iron-on might not remain in place until she outgrows her current size (and would make the seam even stiffer), so I would suggest hand sewing it in place...the satin feels so soothing!

When she has outgrown her current size, another suggestion might be to purchase one size too large and sew a new seam 1/2" inside the existing seam - and then cut the existing "itchy" seam out.
Hope this helps