unfortunately, looks like the answer is no.
I've trawled a lot of milk bottles, but not finding any with what appears to be transfer printed etched work ............. very commonly older bottles show embossing of the glass (raised) decoration/wording, and coming forward a little in time this often changes to decoration by use of coloured enamels - to advertise makers or sellers name etc., and this method proved able to withstand the repeated washing of milk bottles for re-use.
I don't think this is an example of sand blast work, it looks too smooth and the edges of the image appear too sharp, and it's not an example of needle etch. Transfer printed etched work was commonplace toward the end of the C19 and on into the C20 - it was cheap and applied easily to glass surfaces - won't go into the method as it would take too long to explain etc., but it appears on commemorative wares, drinking glasses to advertise the name of a hotel for example, and items of commercial use where corporate advertising was required.
Generally older bottles are straight sided - not tapered like this, so this is very unusual and to have the acid etch of milking maid is doubly good.
If you read the web sites on these things the impression is that swing stoppers gave way to card or paper tops around c. 1900 ish, and none of them goes back beyond c. 1875. Perhaps if you can decipher the breed of cow and discern any particular ethnicity in the clothing you might work out the origin of your bottle.

At a guess I'd suggest this was a little pre WW I - but others may have better informed opinions.
How did you acquire this one? Assume there's lot of wear on the base.