Analysing Jane Austen’s spelling in her letters, I found the plural Turkies rather than Turkeys as we spell it today:

he hopes all your Turkies & Ducks & Chicken & Guinea Fowls are very well (letter 21)

We are just beginning to be engaged in another Christmas Duty, & next to eating Turkies, a very pleasant one, laying out Edward’s money for the Poor (letter 77).

The spelling Turkeys does not appear in the letters. I wanted to know how common this spelling was at the time, and consulted the OED Online. There we find under “Forms”:
“Also 15–16 turkie, 15–17 turky. Pl. turkeys, formerly turkies. .” But what does “formerly” mean, and when did the old practice end? Going through the quotations I found that the plural turkies did not occur beyond the 17th century.

My next step was ECCO, and a keyword search produced 1686 results, throughout the 18th century. My favourite source from the year 1800 is The farmer’s boy; a rural poem, in four books, by Robert Bloomfield (1766-1823), an “English labouring class poet“:

For pigs, and ducks, and turkies, throng the door, /And sitting hens, for constant war prepar’d (p. 12).

The spelling in this quotation should most probably be attributed to the publisher (the printer or typesetter) of the book, rather than to Bloomfield himself.

The entry for Turkey, as Fiona McPherson explains in her comment to this post, has not yet been revised, and more precise information on the spelling history of the word will eventually be provided based on the available evidence. As for Jane Austen’s usage, I am now able to conclude that it was, to begin with, no spelling error, as she used the same spelling twice. (I found in my study of her language that she is actually quite a good speller, though an idiosyncratic one.) And more importantly, the plural Turkies was still quite common at the time.