Alright, looking to revive some of LJ's reformed community:
Can infants have faith? I would contend they can.
Faith is more trust than intellectual cognition. The demons intellectually understand God exists but are not saved. Likewise a child can trust his mother without truly understanding much about her. Through the word and sacraments, in the same way we speak to infants eventually teaching them speech, God uses them to build faith even in infants.
BTW, note this doesn't assume paedobaptism, though it may make more sense. You could argue that infants may be regenerate but should be baptized until they demonstrate their faith.