The "ladybird, ladybird fly away home" rhyme probably didn't mean what we now think it means.

Lina Eckenstein's 1906 book Compartive Study of Nursery Rhymes {London, Duckworth & Co.} has a pretty extensive section on the meaning of the "Ladybird, ladybird, fly away home" rhyme.
{pages 91-106}. Because this book is difficult to find, I'll post extensively from that section:

"The ladybird is the representative amoung ourselves of a large class of insects which were associated with the movement of the sun from the earliest times. The association goes back to the kheper or chafer of ancient Egypt, which has the habit of rolling along the ball that contains its eggs. This ball is identified as the orb of the sun, and the kheper was esteemed as the beneficient pwere that helped to keep it moving.   

A like imprtance attached to the chafers that had the power of flying, especially to the ladybird {Coccinella septem punctata}. In India the insect was called Indragopas that is "protected by Indra". The story is told how this insect flew too near the sun, singed its wings, and fell to earth. [citation given].

In Greece the same idea was embodied in the myth of Ikaros, the son of Daedalus, who flew too near the sun with the wings he had made for himself, and falling into the sea, was drowned. Already the Greeks were puzzled by this myth, which found its reasonable explanation in describing Ikaros as the inventor of sails. He was the first to attach sails to a boat, and sailing westward, he was borne out to sea and perished.

Among ourselves the ladybird is always addressed in connection with its power of flight. It is mostly told to return to its house or home, which is in danger of being destroyed by fire, and warned of the ruin threatening its children if it fails to fly. But some rhymes address it on matters of divination, and one urges it to bring down blessings from heaven.

The rhyme addressed to the ladybird first appears in the nursery collection of 1744, where it stands as follows:
1. Ladybird, ladybird, fly away home.
   Your house is on fire, your children will burn.   

Many variations of the rhyme are current in different parts of the country, which may be tabulated as follows,
[18 additional English variations were given. Some examples are]

2. Lady cow, lady cow, fly away home
   Your house is on fire, your child all roam
[1892, p. 326]

5. Ladybird, ladybird, eigh thy way home,
   Thy house is on fire, thy children all roam,
   Except little Nan, who sits on her pan
   Weaving gold laces as fast as she can.
[Lancashire, 1892, p. 326]

6. Ladybird, ladybird, fly away home,
   Your house is on fire, your children are home.
   They're all burnt but one, and that's little Ann.
   And she's crept under the warming pan.
[Rusher's Series]

11. Fly, ladybird, fly!
    North, south, east, or west,
    Fly to the pretty girl that I love the best.
[1849, p. 5]

18. God A'mighty colly cow, fly up to heaven;
    carry up ten pound, and bring down eleven.
[Hampshire, 1892. p. 327

19. This ladybird I take from the grass.
    Whose spotted back might scarlet red surpass.
    Fly ladybird, north, south, east, or west,
    Fly where the man is found that I love best.
[M.; p. 417, citing Brand]

-snip-

The author then provides some "foreign parallels" for this rhyme, and then writes the following paragraph:

"Mannhardt was of the opinion that the ladybird rhyme originated as a charm intended to speed the sun across the dangers of sunset, that is, the "house on fire" or welkin of the West...

[And there my photocopies of those pages ends. The next page I have is page 106 where Lina Eckenstein begins to discuss the foreign parallels to the rhyme "Humpty Dumpty"]...