I was thinking maybe fop or dandy. I looked up puppyism and it is as you say conceit from Webster's 1913

1. Extreme meanness, affectation, conceit, or impudence.

I looked up dandy because I was was curious and found from the 1828 Webster's this funny definition.
DAN''DY, n. In modern usage, a male of the human species, who dresses himself like a doll and who carries his character on his back.

I'm guessing a fop or dandy is mostly concerned with their outward appearance, while a coxcomb or puppy is all that and more.

Elinor in ch. 36 has these thoughts right at their introduction.
He addressed her with easy civility, and twisted his head into a bow which assured her as plainly as words could have done, that he was exactly the coxcomb she had heard him described to be by Lucy.

I think it is funny too, how he thinks he's so superior that he advises all the people around him. I think it's a similarity that Mr. Knightley sees in Frank Churchill: practised politician, who is to read every body's character.
To his mother about Edward:
"If you had only sent him to Westminster as well as myself, instead of sending him to Mr. Pratt's, all this would have been prevented.' This is the way in which I always consider the matter, and my mother is perfectly convinced of her error."

Look at this quote by Pope from Webster's 1913 dictionary for coxcomb:
Some are bewildered in the maze of schools, And some made coxcombs, nature meant but fools. Pope.

So much for Robert Ferrar's education. :-)

Anyway, Robert is free with his advice.
'My dear Courtland,' said I, immediately throwing them all into the fire, 'do not adopt either of them, but by all means build a cottage.' And that, I fancy, will be the end of it.

"My dear Lady Elliott, do not be uneasy. The dining parlour will admit eighteen couple with ease; card-tables may be placed in the drawing-room;.... blah, blah blah

Elinor agreed to it all, for she did not think he deserved the compliment of rational opposition.