This -ish suffix itself isn't actually "informal" (foolish, childish, devilish, for example, are well-established).
According to OED, the usage extended from nouns such as fool, child, devil centuries ago, to include adjectives - initially with colours (bluish, greenish, etc.), but "in later use also with other adjectives, and now, in colloquial use, possible with nearly all monosyllabic adjectives, and some others".
OED's definition for the suffix when applied to a noun says...
Of or belonging to a person or thing; of the nature or character of.
...
In recent colloquial and journalistic use, -ish has become the favourite ending for forming adjs. for the nonce (esp. of a slighting or depreciatory nature) on proper names of persons, places, or things, and even on phrases, e.g. Disraelitish, Heine-ish, Mark Twainish, Micawberish, Miss Martineauish, Queen Annish, Spectator-ish, Tupperish, West Endish; all-over-ish, at-homeish, devil-may-care-ish, how-d'ye-doish, jolly-good-fellowish, merry-go-roundish, out-of-townish, and the like.
Obviously some of the more "unusual" versions could well be called "informal", and because there's often the possibility of a more "scholarly" alternative (Micawberesque rather than Micawberish, for example), some people may feel it's inherently a bit informal. But I don't really think so - it's just that the suffix is so "productive" people naturally make use of it to informally create nonce words as and when they want.
As OP seems to have discovered, rather is often used conjunction with -ish forms (including "rather childish" as well as "rather Barbieish"). Usually, it will have the sense of to some extent, or in some way, but in some contexts it might have more of the "comparative" meaning to a greater extent...
"I wouldn't say she's 'Barbieish' - rather 'Dolly Partonish', to my mind."
EDIT: Because it's become increasingly common in recent years, I'll just make special mention of -ish as used to impart a certain "vagueness" to times...
"Drop by my office tomorrow afternoon. Three-ish would be fine."
"I've nearly finished coding the new app. It should be ready for testing Wednesday-ish"
In fact, this usage has become so common, the suffix can sometimes be used on its own...
"Hi. I'm just calling to make sure you're coming early to help prepare for my party tonight."
"Stop worrying! I told you before I'll definitely be there"
"Great! See you at 6 then!"
"Ish." [hangs up]
(where that final word effectively means "I'll arrive about 6, but probably later than you're expecting.")
The word "honeykins" uses two suffixes to make it more endearing: "-kin" and "-s".
-kin is an English suffix that was used in the olden days to form diminutive forms of nouns. There are still several dozen words in the language that were formed using this suffix. The more known are pumpkin, catkin, napkin, the less known are ladykin, pannikin.
It has a curious etymology, let me quote from Wiktionary:
See - it's Germanic in origin: compare with German "Mädchen", "a girl". It is composed of the root "Magd"/"Maid", "female servant", and the diminutive suffix "-chen".
Another interesting bit, from "A History of British Surnames" by Richard McKinley, page 100:
It turns out Richard Dawkins has this suffix too! Live and learn.
The linguistic term for a diminutive, endearing calling name is hypocorism (Wikipedia):
A hypocorism (/haɪˈpɒkərɪzəm/; from Greek ὑποκορίζεσθαι hypokorizesthai, "to use child-talk"), also known as a pet name or calling name, is a shorter or diminutive form of a word or given name, for example, when used in more intimate situations as a nickname or term of endearment. However, shortening of names is certainly not exclusive to terms of affection; indeed, in many cases, a shortened name can also be used to intimidate or humiliate. The ambiguity would need to be clarified by context.
According to Wiktionary, the suffix -s has 5 meanings, and one of them is hypocoristic:
Diminutive suffix:
Babs; moms; pops; homes; Toots
It is considered to be a shortened form of the hypocoristic diminutive suffix -sy.
In the "Cambridge Grammar of the English Language" by Huddleston and Pullum, both "-kin" and "-s" are mentioned briefly in Unit 5.2.1 "Evaluative morphology: Diminutives":
The suffix -s also occurs after diminutive -ie in such playground words as onesies, twosies, widesies: it is doubtful whether it is here marking plural number. In addition it is found in various terms of address, such as ducks or Pops.
Best Answer
Adding an '-ish' at the end of a word is generally done in informal contexts, mostly to make the reference sound deliberately vague and approximate. (Source)
Here, the speaker has added the suffix because he isn't completely sure of the similarity with the posterior value.
You can add the suffix to words, to bring about a hint of uncertainty. For example,
Update
As pointed out by Michael Kay, if the adjective points to an extreme, then '-ish' implies less extreme; 'small-ish' is less small than small; 'cold-ish' is less cold than cold; 'same-ish' is less similar than same. So '-ish' not only conveys approximation but can also assign less of the characteristic than if "-ish" were omitted.