I find both acceptable. As you say, happiness is uncountable, which would mean zero article. However, an adjectival attribute often causes an indefinite article to be used before nouns that don't normally take an article — or take the definite article.
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AnonymousI'm feeling a great happinessI am experiencing a particular quality of happiness, or a particular occasion of feeling happy.
AnonymousI'm feeling great happinessI am very happy (in the same general way that I feel happy).