Found sheet music to "DOWN BY THE RIVERSIDE" by John J. Nolan, 1902, at American Memory. Published by G. W. Setchell, Boston.
It has no relationship to the "bright-eyed doll" song. No mention of 'Toorish.'

Here is the chorus, which is sung to waltz tempo:

Down by the riverside,
You said you'd be my bride.
And though years have flown,
Yet I am here alone
Waiting my love for you,
Say that you're not untrue,
You'll come what e'er betide,
Down by the riverside.

I won't bother to post the verses to the song, which may be found at American Memory.

http://scriptorium.lib.duke.edu/sheetmusic/b/b03/b0338/
Down By

Joe F, as you say, the "bright-eyed doll" may be much later.