From a Dogmatic Catholic perspective, what is the eternal destination of an unbaptized embryo? This dogmatic statement from the Council of Trent makes it Crystal Clear that we inherit sin from Adam.


  If any one asserts, that the prevarication of Adam injured himself alone, and not his posterity; and that he lost for himself alone, and not for us also, the holiness and justice, received of God, which he lost; or that he, defiled by the sin of disobedience, has only transfused death, and pains of the body, into the whole human race, but not sin also, which is the death of the soul, let him be anathema; inasmuch as he contradicts the apostle, who says: By one man sin entered into the world, and by sin death, and so death passed upon all men, in whom all have sinned.


The Inspired Author shows us that the infant is not an exception.


  Therefore behold I was conceived in iniquities; and in sins did my mother conceive me. Psalms 51:5


Is there a infallible dogmatic statement from the Catholic Church addressing the eternal destination of the deceased Embryo as a result of his original sin?
Catechism of the Catholic Church (CCC)- 1250 Born with a fallen human nature and tainted by original sin, children also have need of the new birth in Baptism to be freed from the power of darkness and brought into the realm of the freedom of the children of God, to which all men are called. The sheer gratuitousness of the grace of salvation is particularly manifest in infant Baptism. The Church and the parents would deny a child the priceless grace of becoming a child of God were they not to confer Baptism shortly after birth.


So, the Catechism follows the teaching of Trent (of course) that all have a fallen human nature and all are in need of water baptism to effect the new birth.

What happens, however, if an infant isn't baptised?


  CCC- 1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them,"64 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.


To add:


  
  Before Vatican II, in the Latin Church, there was no Christian funeral rite for unbaptised infants and such infants were buried in unconsecrated ground. Strictly speaking, there was no funeral rite for baptised infants either, but in their case a Mass of the Angels was celebrated and of course they were given a Christian burial. Thanks to the liturgical reform after the Council, the Roman Missal now has a funeral Mass for a child who died before Baptism, and there are also special prayers for such a situation in the Ordo Exsequiarum. Though the tone of the prayers in both instances is noticeably cautious, it is now the case that the Church liturgically expresses hope in the mercy of God, to whose loving care the infant is entrusted. This liturgical prayer both reflects and shapes the sensus fidei of the Latin Church regarding the fate of unbaptised infants who die: lex orandi, lex credendi. Significantly, in the Greek Catholic Church there is only one funeral rite for infants whether baptised or not yet baptised, and the Church prays for all deceased infants that they may be received into the bosom of Abraham where there is no sorrow or anguish but only eternal life.