Here's my transcription of the Carter Family recording, with help from the Carter Family Songs Website:

LITTLE MOSES

Away by the river so clear, the ladies were winding their way;
And Pharaoh's little daughter stepped down in the water
To bathe in the cool of the day.
   Before it was dark she opened the ark
   And found the sweet infant was there.
   Before it was dark she opened the ark
   And found the sweet infant was there.

And away by the waters so blue, the infant was lonely and sad,
She took him in pity and thought him so pretty,
And it made little Moses so glad.
   She called him her own, her beautiful son,
   And sent for a nurse that was near.
   She called him her own, her beautiful son,
   And sent for a nurse that was near.

   [INSTRUMENTAL BREAK]

And away by the river so clear, they carried the beautiful child
To his own tender mother, his sister and brother,
Little Moses looked happy and smiled.
   His mother so good done all that she could
   To rear him and teach him with care.
   His mother so good done all that she could
   To rear him and teach him with care.

   [INSTRUMENTAL BREAK]

And away by the sea that was red, little Moses, the servant of God,
While in Him confided, the sea was divided,
As upward he lifted his rod.
   The Jews stepped across while Pharaoh's host*
   Was drownded in the waters and lost.
   The Jews stepped across while Pharaoh's host
   Was drownded in the waters and lost.

And away on the mountain so high, the last one that ever might see,
While in Him victorious, his hope was most glorious,
He would soon o'er the Jordan be free.
   When his labor did cease, he departed in peace,
   And rested in the heavens above.
   When his labor did cease, he departed in peace,
   And rested in the heavens above.


From the Carter Family recording on the Harry Smith Anthology of American Folk Music
This version is almost the same as the unattributed version in the Digital Tradition, with just a few words different.

*could be: "The Jews they could cross while Pharaoh's host..."

This version can be found, with tune, in Asch/Dunson/Raim, Anthology of American Folk Music (Oak Publications, 1973), p. 74, "Little Moses" (1 text, 1 tune)

Also in John Cohen, Mike Seeger, and Hally Wood; Old Time String Band Songbook (Oak Publications, 1964, 1976). Previously published as The New Lost City Ramblers Songbook., page 128, with tune.