The first is, but the second is not.
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MustAskIs it because the word 'experience' is a non-count noun?It is supposed to be in your sentences, but it isn't always. You can have a single experience: "Climbing Kilimanjaro was an exhilarating experience for us." Your second sentence, "I've got a one-month experience as a doctor?", is wrong because you tried to use it that way.