Eye protection for child in bicycle child carrier
What is the eye protection protecting against?


Stones up off your back wheel - then install a full mudguard/fender. 
UV light?  Then kid sunglasses should do the trick
Bees bugs and insects?  Again sunglasses
Nasty sights on the roadway?  Really dark sunglassess.
Aero advantage?   a fully aero helmet and skinsuit will be required.
Or try nothing and see how it goes - kids don't need to be cotton-wooled all the time, just gotta pick the times.


Note, that second-last one is humour.