Can we recite ayat ul-Kursi on an infant?

Yes. It is not about prescribed, but you can - for those who can. It is just like the three Quls for example. You know your kids cannot do it. So people have commonly recited themselves and then wiped it on kids until they are able to do it themselves.[1]

Do you have to do that? Mostly it is based on ijtihaad view of scholars.

Reference:

[1] http://islamqa.info/en/6092