I get this question often. I respect the concerns it arises from. Simply stated, the reason why Protestant Christians have traditionally withheld communion from baptized infants is that, unlike Passover, the Lord's Supper involves more than typology. It entails—wait for it—communion. Let me explain.
The Old Testament Passover feast predates the incarnation of the Son. As such, its significance was principally typological, pointing to the Lamb of God yet to come. The Lord's Supper, by contrast, is a spiritual participation in the now-incarnate Lord Jesus. By means of the sacrament, we feed on Christ's true human body by faith, not merely anticipate it. For that reason, the Supper is appropriately apprehended only by those capable of self-assessment (“examine yourselves”), and its benefits are realized through conscious communion in faith. I would no more give the Supper to a covenant infant, than feed it to a comatose adult Christian. Neither may be expected to sensibly commune with Christ by faith while in that state. As I understand it, communion is an act of conscious participation in spiritual realities, and of covenant renewal through faith.
Baptism, on the other hand, is a rite of initiation into the visible administration of the covenant community. On its top-most level, it is not a picture of your personal conversion. Rather, it signifies Christ's death, burial, and resurrection on behalf of the church throughout time, and applied historically by the Spirit. The function of baptism for infants is to visibly unite them with the Christian community, and to direct their faith at whatever point in life God regenerates them. In this respect, baptism functions identically with circumcision. The cut foreskin was “a seal of the righteousness which Abraham had through faith,” yet it was given to his infant son, to lead Isaac to the source of true righteousness—faith in Messiah (Rom 4:11).