Both the Old and New Testaments draw standards in regards to this means of grace; In the Old, the passover. In the New, the Lord’s Supper.

“However, it should be noted that in that very article Keidel himself admitted, “at a certain age the Jewish male became responsible to God for observing this ordinance of the covenant . . . .Aboth 5:21 makes thirteen the age at which children become subject to commandments of this kind. Thirteen was probably the age at the time of Christ. But if thirteen was the age of accountability, why is Christ mentioned as having gone up at the age of twelve? It may be because Luke wanted to show that Christ’s parents were training their Son in observing the fast connected with the Passover (Pesachim 99b) — a kind of training Yoma 82a says should be done a year or two beforehand . . . . The phrase: `according to the custom of the Feast’ (Luke 2:42), therefore, could refer . . . to the requirement of going at the age when one becomes an adult . . . . Deuteronomy 16:16.” This is quite an admission from one who advocates child communion. Keidel allows that child communion prior to catechizing wasunknown in the Passover of Christ’s day.

It is a well established belief among Reformed Christians that New Testament baptism has replaced Old Testament circumcision. It is also well established that Old Testament Passover prefigured (and was replaced by) New Testament Communion. Passover was an Old Testament covenantal and sacramental meal. There are both similarities and differences between the former sacrament and the current sacrament.”

“The night before God delivered Israel from Egypt He gave them the Passover meal (Numbers 33:3). Today in most Jewish homes a so-called Passover meal (or seder) is eaten by the entire family, including even some very young children if they happen to be present. Yet, we should not let this practice by itself influence our thinking. Rather, we should return to Scripture to see how and why the Passover was instituted by God, and what aspects of Passover are carried forward into the new covenant meal of the Lord’s Supper.”

“In Exodus 12:43ff., Moses describes “the ordinance of the Passover.” First, no strangers may eat it because it is a covenantal meal (43). Second, slaves may eat the meal only after they have been circumcised — thus receiving the sign of the covenant (44). Third, it is no ordinary meal (as a so-called agape feast would be), but a sacramental meal. The elements are therefore not to be treated as ordinary or common food (46). Finally, a stranger may partake if and after he accepts covenantal responsibilities (48-49). In verse 48, all his males must be circumcised, but only he (as an adult male covenantal head of the household) draws near and partakes. Upon drawing near and partaking of the sacramental meal, he is subject to the very same laws of God as the covenant people (49).”

“What we have learned from Exodus, Numbers, and II Chronicles so far is that Passover was not eaten indiscriminately by every member of the nation. In fact, at least three things could exclude someone from eating the meal: uncircumcision (Exodus 12:48), ceremonial uncleanness (Numbers 9:6; cf. 5:2), and an unyielded heart (II Chronicles 30:8).

But a person could not simply and independently determine on his own whether or not to eat the meal. For the same sanction against uncircumcision found in Genesis 17:14, that of being cut-off from the covenant community, is also given against the willful non-communer in Numbers 9:13. This is a covenant meal and is thus to be eaten covenantally.”

24 And ye shall observe this thing for an ordinance to thee and to thy sons for ever. 25 And it shall come to pass, when ye be come to the land which the Lord will give you, according as he hath promised, that ye shall keep this service. 26 And it shall come to pass, when your children shall say unto you, What mean ye by this service? 27 That ye shall say, It is the sacrifice of the Lord’s passover, who passed over the houses of the children of Israel in Egypt, when he smote the Egyptians, and delivered our houses. And the people bowed the head and worshipped. 28 And the children of Israel went away, and did as the Lord had commanded Moses and Aaron, so did they.”

The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Ex 12:24–28.

The above quotes taken from Dr. Richard Bacon’s paper entitled: What mean Ye?

27 Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. 28 But let a man examine himself, and so let him eat of that bread, and drink of that cup. 29 For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord’s body. 30 For this cause many are weak and sickly among you, and many sleep. 31 For if we would judge ourselves, we should not be judged. 32 But when we are judged, we are chastened of the Lord, that we should not be condemned with the world.
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), 1 Co 11:27–32.

The stem word is δοκή (δοχή), “watching” (whence δόκιμος, as ἄλκιμος from ἀλκή, μάχιμος from μάχη). δόκιμος as an adj. both of person and object thus denotes1 a. “tested in battle,” “reliable,” “trustworthy,” b. “a man who is tested, significant, recognised, esteemed, worthy” (e.g., πολίτου δοκίμου ἡ ἀρετὴ εἶναι τὸ δύνασθαι καὶ ἄρχειν καὶ ἄρχεσθαι καλῶς, Aristot. Pol., III, 4, p. 1277a, 26f.; Λυκούργου, τῶν Σπαρτιατῶν δοκίμου ἀνδρός, Hdt. I, 65: καλέσας δώδεκα τοὺς δοκιμωτάτους, Jos. Vit., 55), or “an object which is tested, genuine or valuable” (τούτους δοκίμοις ἵπποις καὶ ὅπλοις παρεσκευασμένους, Xenoph. Oec., 4, 7); it is particularly used of metals, as consistently in the LXX, Gn. 23:16; 1 Ch. 28:18; 29:4; 2 Ch. 9:17; and finally: πρὸς δαιμονιαζομένους Πιβηχέως δόκιμον, for a reliable means of magic, Preis. Zaub., IV, 3007, cf. I, 246.

Gerhard Kittel, Geoffrey W. Bromiley, and Gerhard Friedrich, eds., Theological Dictionary of the New Testament (Grand Rapids, MI: Eerdmans, 1964–), 255.

As well, membership and baptism is a prerequisite. So, in regard to the OP, the child should be of age where he has been baptized and is an actual member of the church. In being baptized, the child has been adequately catechized on the scripture and doctrine. On being baptized and confirmed by the leadership and federal head of the family, he has been examined and is a member of the church.