Now a note from many many eye doctors. Your child should be wearing sunglasses! If it's bright enough that you need them then so does your child, yes infants too!
For infants you ca get glasses that have a wrap around band. If you start your children early enough then they don't know any different and it won't be a fight. But really, eye protection from the sun is just as important as skin protection. The absolute best sunglasses will say "polarized" but they are kind of spendy and if you aren't sure you can get your kid to keep them on I'd start with the cheaper ones but make sure they say UVA/UVB protection. (these are from One Step Ahead but I've seen the glasses with the wrap around strap at Target too)