Iran isn't really any more stable than Iraq is. Iran has already meddled enough in Iraq and would only make things worse if they invaded. Iraq needs a stable government and not be overrun with militants. I believe if Iran invaded Iraq it would be a huge threat to world peace, however it may happen if ISIS keeping attacking Iran.
The government of Iraq is an independent country, it should not be invaded by another country, such as Iran. The people of Iraq have the right to live as a free and independent population not under the control of other parties. The Iranians have no legit interest in invading Iran.
Countries should rarely invade other countries. Invasion in an act of war and wars kill everyone except the people they are supposed to kill. Disputes or situations should be handled diplomatically. There is a very simple rule we all learn in kindergarten. That is, treat others as you would like to be treated. It's golden and easy and fuels respect for each other.
Iran should not invade Iraq. If Iran would like to prove themselves, this is the time. Their neighbor is struggling and they could use assistance. If Iran would like to help settle the dispute then they should, but they should not try to capture or control Iraq in the process.