Source: pp 253, 259. With Good Reason, An Introduction to Informal Fallacies (2000 6 ed) by York U. Prof. S. Morris Engel.
[p 253 :] This exercise's instruction = this one.
[p 259 :] 43. The moment Alice appeared, she was appealed to by all three to settle the question, and they repeated their arguments to her, though, as they all spoke at once, she found it very hard indeed to make out exactly what they said.
The executioner's argument was, that you couldn't cut off a head unless there was a body to cut it off from: [1.] that he had never had to do such a thing before, and he wasn't going to begin at his time of life. [End of 1.]
The King's argument was, that anything that had a head could be beheaded, and that you weren't to talk nonsense.
The Queen's argument was, that if something wasn't done about it in less than no time she'd have everybody executed, all round. (It was this last remark that had made the whole party look so grave and anxious.) (Lewis Carroll, Alice in Wonderland)
Conjecture: Please see the one here that pertains to all these exercises.
I have not read this book, but know that Carroll was an excellent mathematician and logician and so might have inserted some clever Informal Fallacies. So have I missed anything?
Anyhow, I can only discern an Appeal to Tradition (as a case of Appeal to Authority (cf. pp 244-245) in 1 above, because the necessity of an action depends not on what the execution did or did not do in the past, but on what is needed now. I do not discern any Logical Fallacies by the King or Queen.