The Carter song "Little Moses" is a combination with songs other than "Moses in the Bulrushes." Belden says that the "Moses in the Bulrushes" he collected in 1905 covers only the first half of the song reported from Tennessee by George Pullen Jackson from Tennessee.
Recorded from the singing of Miss W. A. Drumgoole as she remembered it sung in 1890 by Mr. Tate, stage driver from Beersheba to Beersheba Springs on Cumberland Mountain. The full text from Mrs. Maggie Haun (called "defective" by Jackson).
The Jackson text:

The ladies were wending their way
As Pharo's daughter stepped down to the water
To bathe in the cool of the day.
Before it was dark she opened the ark
And found that the sweet infant was there.

She took him in pity and thought him so pretty,
That made little Moses so glad.
She called him her own, her beautiful son,
And sent for a nurse that was near.

By the side of the river so clear
They *earned that beautiful child *sic
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 hear [rear?] him and teach him with care.
Then away by the sea that was red
Stood Moses the servant of God.

While in him confided the deed [dead sea?] was divided
While upward he lifted his rod.
The Jews safely crossed while Pharo's host
Was drounded in the water and lost.

Then away to the mountain so high
Stood Moses with trembling an' awe,
With lightning and thunder, great signs and wonders,
While God was giving the law.
He wrote it down on two tables of stone
Before he returned to the sky.

Then away on the mountain so high
Stood the last one he ever might see.
While Isreal victorious, his hope was most gloriest,
Would soon over Jordan bbe free.
His neighbors did cease, he departed in peace,
And rest-es in heaven above.

George Pullen Jackson, 1937, "Spiritual Folk-Songs of Early America. Augustin NY.