Celtaddict, here is the 'whither' version from Halliwell, Nursery Rhymes of England, 1846, Ninth Class, Gaffers and Gammers:

CLXXX, p. 91
There was an old woman toss'd up in a basket
Nineteen times as high as the moon;
Where she was going I couldn't but ask it,
For in her hand she carried a broom.

Old woman, old woman, old woman quoth I,
O whither, o whither o whither, so high?
To brush the cobwebs off the sky!
Shall I go with thee? Aye, by and by.

From 'Infant Institutes,' 8vo, London, 1797, p. 15.

Halliwell is on line, but I copied it in my files and don't have the address. A look in google should find it quickly.