Maybe I still misunderstand. I do agree that the question is not spoken as a question, and needs to have an upward intonation at the end. But whether you put "Do" at the beginning of your answer should not matter to Duolingo. The answers
"Do your cats drink milk?"
"Do your cats drink milk"
"Your cats drink milk?"
"Your cats drink milk"
should all be marked correct by Duolingo. If not then it needs to be reported as not accepting your answer.
EDIT: I base this on the fact that I never start questions with "Do" or "Does" or end questions with punctuation (simply because I am lazy) and Duolingo accepts it 99% of the time.
My english is not so good, but I'll try to explain.
In portuguese, we could use TU or VOCÊ to talk about YOU. They have the same meaning, but the grammar rules are different. When you use TU, you have to use the possessive pronoun TEU (male) or TUA (female). When you use VOCÊ, you have to use SEU (male) or SUA (female). To form the plural, you add "s" (TEUS, TUAS. SEUS, SUAS).
Ex: Você tem um gato (you have a cat). Seu gato bebe leite (your cat drinks milk).
Tu tens um gato (you have a cat). Teu gato bebe leite (your cat drinks milk).
As you can see, the two phrases have the same meaning, but are grammatically different.
Olá! You (Você, ou Tu) can choose to use only "você" instead of "tu", because it is most commonly used in Brazil.
In the south of Brazil you use "tu", but there are also those who say "você".
By using "você", it is easier to conjugate verbs. (Everything is easier!)
Você / Possessive: "Seu, seus; Sua, suas".