Here's another (very unlikely, I hope) possibility for what the "aranatus" was: a spider! I certainly hope the woman in the song isn't twining spiders into her hair!

But, for completeness…

In the "Transactions of the Kansas Academy of Science," Vol. XIX, 1905, in the "Biological Section" entitled "A Preliminary List of Kansas Spiders" on page 188, under "Family ARGIOPIDAE." we find the following entry:

Araneus aranatus Walck.
Epeira aranata Walck. Ins. Apt., II, 1837-'47, p. 133.
    Common in the woods about Manhattan [Kansas] in the midsummer months.

The Argiopidae are a family of orb-weaving spiders with eight eyes, and includes many well-known large or brightly colored garden spiders. (Webster's Third New International Dictionary, Unabridged. 2002). Araneus (Aranea) is the genus. Aranatus must therefore be the species. "Walck" refers to some guy named C. A. Walckenaer who set up entire spider-naming systems in the 1840's.