kat, the ditty seems to be old indeed, and inscrutable in its original meaning. Here is a text by the Grimm brothers 1819, translated only in the non-italic parts:

Marienwürmchen, fliege weg! fliege weg!
dein Häuschen brennt! die Kinder schrein!

A complete song is communicated by the Wunderhorn I. 235. The Northern Antiquities I. 322 observe the same custom in England and even the rhyme

Lady-bird, lady-bird, fly and begone!
your house is a-fire and your children at home!

I suspect Arnim/Brentano extemporated on this, adding the contemporary symbolism which praises beautiful art as a means against opression. That "romantic" idea has remained of limited but not negligible power in the Nazi period and still today; think of China, the Arab world, etc.

Note that the Northern Antiquities of 1814 are a good witness for the English verse, but for a "complete song" they can only quote the Wunderhorn version once more:

Indeed, many curious relics of past times are preserved in the games and rhymes found among children, which are on that account by no means beneath the notice of the curious traveller, who will be surprised to find, after the lapse of so many ages, and so many changes of place, languages and manners, how little these differ among different nations of the same original stock, who have been so long divided and estranged from each other. As an illustration of this, which we happen to have most conveniently at hand, we give the following child's song to the Lady-bird, which is commonly sung while this pretty insect is perched on the tip of the fore-finger, and danced up and down. Every child knows the English rhyme,

"Lady-bird, lady-bird, fly and begone,
Your house is a-fire, and your children at home, &c."

The German children have it much more perfect, as well as much
prettier, the English having preserved only the second stanza in their address.

Marienwürmchen, setze dich ...

Although I have partial German roots and currently live in Germany, I am not an expert on German - or English - folklore. The usual suspects may know more. Anyway, it is quite ridiculous to date such verses back to ancient Germanic times; folklore always travelled within Europe at the speed of sound, so-to-speak.