There appears to be no minimum length of residency required since Indiana will issue permits to non-residents:
IC 35-47-2-3
Application for license to carry handgun; procedure
Sec. 3. (a) A person desiring a license to carry a handgun shall apply:
(1) to the chief of police or corresponding law enforcement officer of the municipality in which the applicant resides;
(2) if that municipality has no such officer, or if the applicant does not reside in a municipality, to the sheriff of the county in which the applicant resides after the applicant has obtained an application form prescribed by the superintendent; or
(3)
if the applicant is a resident of another state and has a regular place of business or employment in Indiana, to the sheriff of the county in which the applicant has a regular place of business or employment.
and
IC 35-47-2-4
Qualified or unlimited licenses to carry handguns; fees; exemptions from payment of fees
(f) The superintendent may not issue a lifetime qualified license or a lifetime unlimited license to a person who is a resident of another state. The superintendent may issue a four (4) year qualified license or a four (4) year unlimited license to
a person who is a resident of another state and who has a regular place of business or employment in Indiana as described in section 3(a)(3) of this chapter.
As soon as you become a resident of Indiana, your out-of-state permits become invalid:
IC 35-47-2-21
Recognition of retail dealers' licenses and licenses to carry handguns issued by other states
Sec. 21. (a) Retail dealers' licenses issued by other states or foreign countries will not be recognized in Indiana except for sales at wholesale.
(b) Licenses to carry handguns, issued by other states or foreign countries,
will be recognized according to the terms thereof but only while the holders are not residents of Indiana.
http://www.in.gov/legislative/ic/code/title35/ar47/ch2.html
You become an Indiana resident as soon as you move to Indiana with no other residence in another state:
http://www.in.gov/legislative/ic/code/title9/ar13/ch2.html
IC 9-13-2-78
Indiana resident
Sec. 78. "Indiana resident" refers to a person who is one (1) of the following:
(1) A person who has been living in Indiana for at least one hundred eighty-three (183) days during a calendar year and who has a legal residence in another state. However, the term does not include a person who has been living in Indiana for any of the following purposes:
(A) Attending a postsecondary educational institution.
(B) Serving on active duty in the armed forces of the United States.
(2) A person who is living in Indiana if the person has no other legal residence. (3) A person who is registered to vote in Indiana.
(4) A person who has a child enrolled in an elementary or a secondary school located in Indiana.
(5) A person who has more than one-half (1/2) of the person's gross income (as defined in Section 61 of the Internal Revenue Code) derived from sources in Indiana using the provisions applicable to determining the source of adjusted gross income that are set forth in IC 6-3-2-2. However, a person who is considered a resident under this subdivision is not a resident if the person proves by a preponderance of the evidence that the person is not a resident under subdivisions (1) through (4).
(6) A person who:
(A) is enrolled as a student of a truck driver training school;
(B) has legal residence in another state but is living in Indiana temporarily for the express purpose of taking a course of study from the truck driver training school; and
(C) intends to return to the person's state of residence upon completion of the course of study of the truck driver training school.
