Did Jesus have a physical body before his incarnation? According to the doctrine of the trinity the Son is eternal.  Is this in reference to his divine nature only or the physical and divine?  If it is both physical and divine, then did the body shrink down into Mary?
The doctrine of the Trinity is only about the nature of the divinity of Jesus, whether it's less than or equal to God the Father.  So you are right that the Son is eternal like God the Father.  The council of Nicaea went even further into defining that there is no time when God the Father existed but Jesus did not.

The human nature of Jesus, on the other hand, was a completely different problem called the hypostatic union.  It has to do whether Jesus was 100 percent human &amp; 100 percent God, less than 100 percent human &amp; 100 percent God, whether Jesus truly suffered as a human, whether the union of human and God was mere appearance, etc.  A convenient list of other options of solving the problem can be found here, but the majority of mainstream Christianity have settled on a definition agreed at the Council of Chalcedon since 451 AD.

You can read the details and the development into the final agreement in the wikipedia article, but what was NOT an issue to the Church Fathers was the nature of the birth.  Jesus was in Mary's womb for the usual 9 months just like a normal baby, but it was just the conception that was special (i.e. not through sexual intercourse), but (pardon me for a little colloquial) it's like the Holy Spirit inseminated Virgin Mary's egg in a miracle.

"Shrinkage" was not necessary because before conception Jesus was in heaven with the Father, responsible for the creation of the universe John 1:1. As to Jesus's form in heaven before coming down to earth, we don't know.  But many Christians believe that being conceived as a baby within Mary's womb wasn't the Son of God's "first trip" to earth, and that he had appeared to Abraham (Gen 18) and possibly several others in the Old Testament, although at that time those who saw him thought of him as an angel in bodily form.

At any rate, I agree with curiousdannii's comment that the theology of pre-incarnate Christ's visitations on earth is far less established than the Incarnation itself, and may I add, it's far less critical to be believed as well.  Even if Jesus appeared prior to the virgin birth, as curiousdannii reminded us, the form may not be fully human either, so maybe it's safe to say that probably the answer to your question is a hard NO.  I'm including this wikipedia article on 'Christophany' to round off the answer.

In response to MegaAwp's follow up question on the definite starting point of the physical form of Jesus, I think most Christian theologians agree that God reveals only what is necessary for salvation and for our hope after the second coming, i.e. how we can pass the day of judgment and how we obtain eternal life in a resurrected body, just like Jesus.  

So one of the main purposes of Jesus's assuming human form (besides to fulfill prophecies about the suffering servant, and to become the righteous second Adam who reverses the curse of the fall) was to provide a preview / deposit of hope so we are not too attached to the earthly bodily life, since in the era of the restored heaven and earth, we will have a resurrected body that is BETTER than what we have now.  

In my opinion, the starting point is less important than the ending point.  That is probably why God didn't reveal to us in what form Jesus existed in heaven prior to His incarnation, except to assure us that Jesus is 100 percent God in heaven and earth (doctrine of Trinity), and 100 percent human and 100 percent divine, during his sojourn on earth (doctrine of hypostatic union).