KIds throw up - Fact, especially when travelling - Cabin crew are used to it, or Bl***y well should be!
You dont call up Medlink if a kid throws up as a first thought -
The pax had only just boarded. She was 3 - it was stupid oclock and she was nervous, 1st time flyer - she was fine afterwards.
Shocking treatment of the family.
The only time one would consider an offload (or a divert if en-route) is if the Pax had described they were already, or had been ill (stomach bugs/infection/viruses etc etc) and were flying out of dodgy places...
I cannot see that this was the case here.