My wife and I are going from Belgium to Italy by plane for a week in June.
... how much validity should she have left on her passport.

As a spouse of an EU Citizen, the conditions of the Freedom of Movement, when both are traveling togeather, apply.

The passport must be valid for the duration of the time outside the country of residence (Article 6 (2)).

This should then cause no problems.

DIRECTIVE 2004/38/EC (Freedom of Movement)
Article 6
Right of residence for up to three months

1. Union citizens shall have the right of residence on the territory of another Member State for a period of up to three months without any conditions or any formalities other than the requirement to hold a valid identity card or passport.
2. The provisions of paragraph 1 shall also apply to family members in possession of a valid passport who are not nationals of a Member State, accompanying or joining the Union citizen.

My wife and I are going from Belgium to Italy by plane for a week in June.
... how much validity should she have left on her passport.

As a spouse of an EU Citizen, the conditions of the Freedom of Movement, when both are traveling togeather, apply.

The passport must be valid for the duration of the time outside the country of residence (Article 6 (2)).

With a passport, which expires in October, a trip in June will be no problem.

DIRECTIVE 2004/38/EC (Freedom of Movement)
Article 6
Right of residence for up to three months

1. Union citizens shall have the right of residence on the territory of another Member State for a period of up to three months without any conditions or any formalities other than the requirement to hold a valid identity card or passport.
2. The provisions of paragraph 1 shall also apply to family members in possession of a valid passport who are not nationals of a Member State, accompanying or joining the Union citizen.