There is no one right answer, because it depends on what you are transcribing, and what conventions you are assuming. As a narrow transcription it is almost certainly not correct for any dialect of English spoken north of the Equator, because "c" is [kʰ] and "r" is [ɾ] or [ɹ,ɹʷ]. Assuming that this is a broad, i.e. phonemic transcription, you have to decide (know) what the phonemes are of the particular dialect, and that is very tricky. For example, there is one tradition where the vowel of "sit" is [i] (and the vowel of "seat" is [i:]); another where these words are [sɪt, sit], also [sɪt, si:t], and [sɪt, sɪjt]. The vowels [ʌ] and [ə] are in complementary distribution with [ʌ] only appearing in a stressed syllable: so you could use either [ʌ] or [ə] to represent the phoneme, since it is an abstraction from phonetics, anyhow.
In American English, there are two other pronunciations, [kɹ̩ɹɪdʒ] and [kɹ̩ʷɹɪdʒ], that is, with a syllabic velarized rhotic approximant which is either rounded or not. The presence of a non-syllabic [ɹ] before [ɪ] is not mandatory, so [kɹ̩ɪdʒ] and [kɹ̩ʷɪdʒ] are just a good and easier to type (less stuff). When you get into the analysis, deriving surface forms from underlying forms, it is actually somewhat "simpler" to assume [kɹ̩(ʷ)ɪdʒ], but that simplicity depends on a particular theory of rules.
The version with [ʌ] is also used (phonetically realized) in the US, though not my dialect (I think it's more East Coast). But: it is common to analyze kɹ̩ɪdʒ as deriving from kʌɹɪdʒ, so that syllabic sonorants can be removed from the phonemic inventory (reducing the inventory is a commonly assumed goal of analysis).