I'm afraid that I can't help much with the date, but I can tell you that the tune, played as a polka, has been popular in Scotland, Ireland and England; it also turns up as an Old Time tune in America.  In Ireland it is also known as Tá Boinéad Agam.  There are a number of examples at  JC's Tunefinder, among them the following (first example Irish, second English):

X: 1
T: I have a bonnet trimmed with blue
B: The Songs of Elizabeth Cronin, ed. D=E1ibh=ED =D3 Cr=F3in=EDn
Z: Paul de Grae irtrad-l 2000-09-04
M: 2/4
L: 1/8
W: 1. I have a bonnet trimmed with blue;
W: Why don't you wear it? So I do.
W: [twice]
W:
W: 2. I will wear it when I can;
W: When I'll go away with my fair-haired man.
W: [twice]
W:
W: 3. Open the window, do love, do!
W: Listen to the music playing for you!
W: [twice]
W:
W: 4. [repeat 1st verse]
W:
W: There's also a version quoted from Iona & Peter Opie's book, "The Singing Game":
W:
W: 'I have a bonnet trimmed with blue.'
W: 'Why don't you wear it?' 'So I do.'
W: 'When do you wear it?' 'When I can -
W: When I go out with my young man.
W: My young man's away at sea,
W: When he comes back he'll marry me;
W: Buy me a biscuit, buy a tart,
W: What do you think of my sweetheart?'
K: D
AB/c/ dB | BA F>G | AA GE | DE F2 |
AB/c/ dB | BA F>G | AA GE | ED D2 ||
A,D FB | AA F>G | AA/A/ GG/E/ | DE F2 |
A,D FB | AF F>G | AA/A/ GG/E/ | ED D2 ||

The following is the entry from  The Fiddler's Companion

ALEX DICE. AKA and see "Bonnet Trimmed in Blue," "Cracovienne," "Din Tarrant's," "I Have a Bonnet Trimmed in Blue," "I have a donkey, he wouldn't go," "Jacket Trimmed in Blue," "Kradoviak," "T· boinÈad agam," "Tarrant's," "Walk Jawbone." American, Schottische. USA, Pa. G Major. Standard. AB.  Bayard (1981) identifies this as an international tune, tracing it to the German "Krakovienne" c. 1842-50 printed in Boehme, which was known as "Cracovienne" or "Krakoviak" in the British Isles.  He also states the tune was known as "Walk Jawbone" in the U.S., and that in Roche (Vol. 2, No. 302) it appears as an untitled set-dance. The tune was also known as "Bonnet (or Jacket) Trimmed in Blue" from lyrics associated to it that began: I have a bonnet (jacket) trimmed with blue,...
Bayard (Dance to the Fiddle), 1981; No. 405, pg. 383.

I HAVE A BONNET TRIMMED WITH BLUE [1] (Ta Boinead Agam). AKA - "I Have a Bonnet." AKA and see "Alex Dice," "Bonnet/Jacket Trimmed in Blue," "Din Tarrant's" "I have a donkey, he wouldn't go," "Jacket Trimmed in Blue," "Krakovienne" (Boehme), "T· BoinÈad agam," "Tarrant's," "Walk Jawbone." Irish, American; Polka.  USA, eastern Mass. G Major (Bayard, Breathnach, Mallinson): A Major (Mallinson). Standard. AB (Bayard): AABB (Breathnach, Mallinson). The name comes from the ditty beginning "I have a bonnet (jacket) trimmed with blue."  Sources for notated versions: Mrs. Anastasia Corkery (Cambridge, Mass., 1930's; originally from Co. Cork, Ireland) [Bayard]; whistle, flute and concertina player Michael Tubridy (Ireland) [Breathnach]. Bayard, 1981; Appendix No. 30, pg. 584. Breathnach, Vol. 3, 1985; No. 68, pg. 35. Mallinson (100 Polkas), 1997; No. 29, pg. 12 & No. 60 , pg. 23. Claddagh Records CC27, Michael Tubridy - "The Eagle's Whistle" (1978).
T:I Have a Bonnet Trimmed with Blue
R:2/4
K:A

I HAVE A BONNET TRIMMED WITH BLUE [2]. Scottish, Polka. D Major ('A', 'B', 'C' and 'F' parts) & G Major ('D' and 'E' parts). Standard. AABBCCDDEEFF. A variation of version #1.
Martin, Vol. 1, 1991; pg. 48.

I HAVE A DONKEY, HE WOULDN'T GO. AKA and see "I Have a Bonnet Trimmed with Blue" [1].

JACKET TRIMMED IN BLUE, THE. AKA and see "Bonnet Trimmed in Blue," "Cracovienne Quickstep." Irish, Canadian; Polka. Ireland, West Kerry. G Major (Messer): A Major (Mac Amhlaoibh & Durham). Standard. AABB. Mac Amhlaoibh & Durham, No. 12, pg. 16 (appears as "A Bonnet Trimmed in Blue").  Messer, 1948; No. 57. Messer, 1980; No. 98, pg. 63.

KRAKOVIAK. AKA and see "Krakovienne," "Cracovienne," "Jacket Trimmed in Blue," "Bonnet Trimmed in Blue," "Walk Jawbone" (USA). Scottish, Dance Tune (2/4 time). G Major. Standard. AABB. Known in Germany as "Krakovienne."  In County Donegal, Ireland, this tune (as it appears in Kerr's) was used at house parties to accompany the dance The Berlin Polky (Polka), as remembered by musician Danny O'Donnell. Kerr, Vol. 1, pg. 46, and Vol. 4, No. 419.

WALK JAWBONE [2]. AKA and see "Alex Dice," "Bonnet/Jacket Trimmed in Blue," "Din Tarrant's" "I Have a Bonnet Trimmed with Blue," "I have a donkey, he wouldn't go," "Krakovienne" (Boehme), "T· BoinÈad agam," "Tarrant's."  Old-Time, Breakdown. F Major. Standard. AABB.  Apparently adapted by American black-face minstrels from an Irish melody.  See Irish version in Roche, Vol. 2, No. 302 (appears as "Set Dance").
Walk, jawbone, Jenny, come along.
In come Sally with her bootees on.
Walk, jawbone, Jenny, come along.
In come Sally with her bootees on.
Ford, 1940; pg. 103. Minstrel Songs Old and New, 1879; pg. 210.

The above would tend to suggest that it's not really old enough for your purposes.

Malcolm