It just would turn out that Child was an American and was late 19th century. It also just would be the case that he collected things that had already been collected and has been said to have a third eye or sixth sense that enabled him to ensure that what he collected was truly old. Here, nonetheless, we can hear a current singer of Child ballads and they do seem ancient.
Meanwhile I have also been able to locate another Danish ballad on the Elfin theme (I want to call if “elven”) about which I have long wondered, “Jeg gik mig i lunden,” on going into the woods on a summer’s eve and being seen, and stolen by the elfin king. Frode Veddinge sings it and this is the wikisource on the lyrics, with music. It sounds possibly, terribly ancient at the beginning, but then exhibits that je-ne-sais-quoi of not-quite authenticity. And in fact it was composed by Johan Ludvig Heiberg in 1828 and is the first song in Elverhøj, the Danish national play from the romantic-national period!
Jeg gik mig i lunden en sildig sommerkvæld
og tømte mig et bæger af sprudlende væld.
Men vogt dig, vogt dig, o min pige,
for elverkongen ser dig!Den brusende bølge sprang ud fra grønne høj,
med ét så blev den stille, den flød uden støj.
Men vogt dig, vogt dig …Da tonede luften af sang og strengespil,
tre hvide møer dansed i duggen dertil.
Nu vogt dig, vogt dig …Som dunst over engen, så flygtig til at se,
de trende blev til en, og den ene til tre.
Nu vogt dig, vogt dig …Han selv stod i midten af hines lette sving,
da drog han af sin finger en kostelig ring.
Ja, vogt dig, vogt dig …Jeg greb efter ringen, men han greb om min hånd,
de hvide møer slynged omkring os et bånd.
Ja, vogt dig, vogt dig …Nu bor jeg i højen som elverkongens brud,
og kun når duggen falder, jeg vover mig ud.
Thi vogt dig, vogt dig …
Axé.
coldhearted scientist وداد 
Thanks for the link!
If you want to know more about the ages of the Child Ballads, you might want to check out this discussion:
http://mudcat.org/thread.cfm?threadid=139929&messages=48
My God, how fascinating. I should have gone into ethnomusicology, I think sometimes — it is so interesting to scout these things out.