Yes, it should be 대꾸했다.
Some people think it is 댓구, which means a "matching phrase/stanza", like in poems.
Its correct spelling is actually 대구, but 댓구 is commonly used as it pronounces the same.
(there is also a theory that 대구/댓구 has evolved over time into 대꾸)
Also the last line of the joke is written wrong and it makes no sense.
아, 그 사람 나도 알아요. 아버지는 나이였을 땐 대통령이었잖아요? (wrong)
=> 아, 그 사람 나도 알아요. 아버지(의) 나이였을 땐 대통령이었잖아요? ("는" is taken out)
it means "Ah, I know him. At your age he was the president, wasn't he?".
So the father was scolding the boy saying Lincoln was so hard working when he was at the boy's age. And the boy counters saying "And at your age he was the president (but what are you now in comparison)?".
To me this one seems to be funnier than the others you posted :-)