"What is today's date?"
Translation:Quelle est la date aujourd'hui ?
"Quelle est la date" is only "What is the date?" which isn't the same as "What is today's date?"
A: "L'anniversaire de ma mére est en octobre."
B: "Quelle est la date?"
I suppose in practice/when speaking, "today's date" would be understood implicitly depending on the context, but the two sentences are not always interchangeable.