Can the goat aged 10 months be offered as 'Qurbani' (sacrifice to get closer to Allah)? Goat is healthy and simmilar in size with goats aged 1 year.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is not correct nor sufficient to slaughter a goat of 10 months age as Udhiyah. Al-Udhiya of the goats, according to Muslim scholars should be a Thaniya (one full year old goat and starting the second year).
Imam al-Nawawi (may Allah's mercy be upon him) said: 'There is agreement among scholars of Islam that it is not sufficient to slaughter a goat that which is not Thaniya.'
Ali (RAA) said: 'al-Udhiya of the goat should be Thaniya…..' This is the opinion of al-Ahnaaf, al-Hanabilah and an opinion among al-Malikiya and al-Shafi'iyah. It is also said, according to al-Malikiya and the correct opinion of al-Shafi'iyah, Thaniya should be of two full years old and starting the third.
It is not sufficient nor correct to slaughter the goat you mentioned in your question as Udhiya.
Allah knows best