I found the original version and it goes

A las puertas del cielo

A las puertas del cielo
Venden zapatos
Para los angelitos
Que andan descalzos

Duérmete niño (x3)
Arrú arrú

A los niños que duermen
Dios los bendice
A las madres que velan
Dios las asiste

Duérmete niño (x3)
Arrú arrú

You can find it on "48 berceuses du monde" from Arb Music and you can listen to a sample here or there, it's #7 on the second cd.

Literal translation so you can see the differences between the original and the translation from the book

At the gates of heaven (the sky)
They sell shoes (not "little shoes")
For the little angels
that go/walk shoeless (not "tattered" which is "harapientos")

Sleep, baby,
Lullaby, lullaby

The children who sleep
God bless them
The mothers who watch (meaning "watch over them")
God assists them.

So this "do do" thing has been introduced in English to translate "arrú" (same use of "arrurú" etc) but has no direct relation to the original lyrics. Now, what would be interesting would be to know who translated the Sp. idiom "arrú" into a Fr. idiom "dodo" for an Eng. translation!