Gemüse is the singular form.
It can either mean a single vegetable, or, much more often, vegetables.
(A bit like "food" in English, which can refer to many items at once. Two slices of bread + an apple = "food", not "foods". Similarly, three carrots + ten peas = Gemüse (singular).)
Gemüse is almost always used as a mass noun -- that is, it's grammatically singular but can refer to any quantity.
Grammatically, it's like "food" in English. If you eat three carrots, you have eaten "food" -- you wouldn't usually say "She has eaten foods". You'd use "food" as a mass noun, grammatically singular, to refer to all three carrots at once.
Most often, you don't have just one single vegetable, so Gemüse most often translates as "vegetables" in English -- so I'd translate Das ist Gemüse into English as "Those are vegetables".
"The woman eats vegetable" is not correct.
The noun "vegetable" is countable in English, so in the singular there has to be a determiner before the noun, e.g. "a vegetable" or "the vegetable".
But the German sentence does not have ein Gemüse or das Gemüse, so the German sentence is not treating Gemüse as countable, but as uncountable. (Which is the case 99% of the time.)
So only a translation of "vegetables" makes sense here.