。
She has a small black dog.
Literal
She [topic-は] small black dog [object-を] is-keeping.
飼っている uses ~ている for a persistent state — she owns and keeps a dog as an ongoing fact. 小さな is one of a handful of Japanese adjectives (along with 大きな and おかしな) that can only appear directly before a noun, never as a predicate. You can say 小さな犬 but not *犬は小さなだ — for the predicate position, the regular い-adjective 小さい is required. When stacking adjectives before a noun, い-adjectives like 黒い simply precede the noun without any connector.