Having read some other versions of Alison Gross it seems that toddle round the tree is what happens when she turns him into a worm:

The DT version linked to above has the following

She's turned me into an ugly worm
And gard me toddle around the tree
And aye, on ilka Saturday night
My sister Maisry came to me

With silver basin and silver comb
To comb my head upon her knee
Before I had kissed her ugly mouth
I'd rather have toddled about the tree

and at the end

She changed me again to my ain proper shape
And I nae more maun toddle about the tree

So toddle has the meaning of crawl in this case I'd guess, although in general human terms the crawling stage precedes the toddling stage.