An_Naseeha

A cow needs to be 2 years and above to be quality for Eid Adha khurbaani irrespective of it's size. A cow can be big and not qualified to be slaughtered for Eid.
It's necessary to know the age of the cow...

"Do not slaughter except a musannah (a mature animal), unless it is difficult for you, in which case you may slaughter a jadha'ah (young sheep)." [Sahih Muslim, Hadith 1963]

Scholars, including Imam al-Nawawi, define the term musannah based on the animal species:

Cows/Bulls/Buffaloes: Must be at least 2 full years old.
Camels: Must be at least 5 years old.Goats: Must be at least 1 year old.

Sheep: Must be at least 1 year old, though a 6-month-old lamb is exceptionally permitted if it is healthy and fat.