There probably is an [e] sound in Afrikaans (or wherever we borrowed it from*); and probably the second vowel is closer to a pure [a], unheard in any English word and unused in English phonology. In English a meerkat is just a /'mɪəkæt/ .
PS *Bingo OED:
(subscription, I'm afraid, so no link)Etymology: < South African Dutch meerkat (Afrikaans meerkat), transferred use of Dutch meerkat a long-tailed monkey of the family Cercopithecidae (see mercat n.).
The forms mier-cat, mier-kat, mierkat reflect the Afrikaans variant mierkat (with the first element altered by folk etymology after Afrikaans mier ant, termite).
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