Benjamin.
 

Rachel died giving birth to Benjamin, by who was the newborn baby suckled?

I suspect it was Bilhah.
Rachel had given the slave to Israel............

You are correct in saying that Bilhah, who had been raped by Reuben while Israel was camped at Ephrath, was lactating at that that time, and was able to be the wet nurse for baby Benjamin, as his mother died in Ephrath while giving birth to him.

The Last Testament of Reuben 3: 11-15; For had I not seen Bilhah bathing in a covered place, I had not fallen into this great iniquity. For my mind taking in the thought of the woman's nakedness, suffered me not to sleep until I had wrought the abominable thing. For while Jacob our father had gone to Isaac his father, when we were in Eder, near to Ephrath in Bethlehem, Bilhah became drunk and was asleep uncovered in her chamber. Having therefore gone in and beheld her nakedness, I wrought the impiety without her perceiving it, and leaving her sleeping I departed. And forthwith an angel of God revealed to my father concerning my impiety, and he came and mourned over me, and touched her no more.

The last Testament of Benjamin 1: 1; The record of the words of Benjamin, which he set forth to his sons, after he had lived a hundred and twenty years. And he kissed them, and said: As Isaac was born to Abraham in his hundredth year, so also was I to Jacob. Now since Rachel died in giving me birth, I had no milk; therefore I was suckled by Bilhah her handmaid. For Rachel remained barren for twelve years after that she had borne Joseph.

Bilhah the mother of Dan and Naphtali, who were born before Joseph, had remained barren longer than Rachel, who died near to Ephrath in Bethlehem.

The Bethlehem in the land of Judah, did not exist in the 17th century when Jacob and his family were living in the land of Shechem, the Bethlehem where Benjamin was born, was the Bethlehem in the land that would later be allocated to the tribe of Zebulun.

Isaiah 9: The land of the tribes of Zebulun and Naphtali was once disgraced, but the future will bring honour to this region, from the Mediterranean eastwards to the land on the other side of the Jordan, and even to Galilee itself, where the foreigners live.

The people who walked in darkness have seen a great light. They lived in a land of shadows, but now light is shining on them.

You have given them great joy, LORD; you have made them happy. They rejoice in what you have done, as people rejoice when they harvest their corn or when they divide captured wealth.

For you have broken the yoke that burdened them and the rod that beat their shoulders.

You have defeated the nation that oppressed and exploited your people, just as you defeated the army of Midian long ago. The boots of the invading army and all their bloodstained clothing will be destroyed by fire. A child is born to us! A son is given to us!
And he will be our ruler. He will be called, “Wonderful Counsellor”, “Mighty God”, “Eternal Father”, “Prince of Peace”.

His royal power will continue to grow; his kingdom will always be at peace. He will rule as King David's successor, basing his power on right and justice, from now until the end of time.

The LORD Almighty is determined to do all this.

Deuteronomy 33: 12; About the tribe of Benjamin he said: “This is the tribe the LORD loves and protects; He guards them all the day long, And he dwells in their midst.”

Psalms 68: 24-27; O God, your march of triumph is seen by all, the procession of God, my king, into his sanctuary.

The singers are in front, the musicians are behind, in between are the young women beating the tambourines.

“Praise God in the meeting of his people; praise the LORD, all you descendants of Jacob!”

First comes Benjamin, the smallest tribe, then the leaders of Judah with their group, followed by the leaders of Zebulun and Naphtali.

Knowing that Benjamin, was the only one of the 12 sons of Israel to have been born near Bethlehem in the land that would be allocated to Zebulun, who do you think that Isaiah is referring to in that passage?