Hold on! The expression is older than that Punch cartoon.

From "Polite Conversation"* in The Works of the Rev. Jonathan Swift, D.D., Dean of St. Patrick's, Dublin, 1801, vol. 8, page 302:

Miss. Lord! I have torn my petticoat with your odious romping; my rents are coming in; I 'm afraid I shall fall into the ragman's hands.
Neverout. I'll mend it, miss.
Miss. You mend it! go, teach your grannam to suck eggs.

* The full title of this work is "A Complete Collection of Genteel and Ingenious Conversation, According to the Most Polite Mode and Method Now Used at Court, and in the Best Companies of England. In Three Dialogues. By Simon Wagstaff, Esq." The whole work seems to be a satire on the use of clichés and catch phrases.


From Lexicon Balatronicum: A Dictionary of Buckish Slang, University Wit, and Pickpocket Eloquence By Francis Grose, Hewson Clarke, 1811, page 91:

GRANNY. ... Go teach your granny to suck eggs; said to such as would instruct any one in a matter he knows better than themselves.

From The history of Tom Jones, a foundling By Henry Fielding, 1820, page 422:

I remember, my old schoolmaster, who was a prodigious great scholar, used often to say, Polly matete cry town is my daskalon. The English of which, he told us, was, That a child may sometimes teach his grandmother to suck eggs.

(As Tom Jones is a satirical novel, I would not advise taking this "translation" too seriously.)