Moses' Age when moving to house of Pharaoh? How old was Moses when he went to live with Pharaoh's daughter?
Most likely just after being weaned from the breast.  


  Pharaoh's daughter said to her, “Take this baby and nurse him for me, and I will pay you.” So the woman took the baby and nursed him. When the child grew older, she took him to Pharaoh's daughter and he became her son. She named him Moses, saying, “I drew him out of the water.”  Exodus 2:8-10 NIV


Since the princess was only paying for nursing services and she wanted a son badly, once her milk dried up baby Moses goes back to the new Pharaoh's daughter mommy at the ripe old age of 6 months-ish.