To expound a bit on Tony's answer, the temple was built in Jerusalem which was in Judah. "Sanctuary" for qadosh is a bit unusual and most likely included for brevity -- a better translation would be "holy place". NICOT has a better translation:
Judah was his holy place,
Israel his dominion.
From the NICOT commentary:
The two cola of vv. 1 and 2 are parallel expressions: Israel and house
of Jacob, Egypt and a people of a different language in v. 1; Judah
and Israel, holy place and dominion in v. 2. The word translated here
as holy place is qād̠ôš, from a root which means “to be devoted, set
apart.” The word translated as dominion is from the root māšal,
meaning “to rule over, to reign.” The two cola summarize two important
aspects of God’s role in the life of ancient Israel: the holy one in
the midst of the people (see Hos. 11:9); and the one ruling over the
people (see Deut. 33:5). Interestingly, neither of the names for
Israel’s God, ʿelōhîm and YHWH, appears in the first verses of Psalm
114, perhaps giving further strength to the idea that Psalm 113 is to
be read as a prelude to Psalm 114. deClaissé-Walford, N. (2014). Book Five of the Psalter: Psalms 107–150. In E. J. Young, R. K. Harrison, & R. L. Hubbard Jr. (Eds.), The Book of Psalms (p. 851). Grand Rapids, MI; Cambridge, U.K.: William B. Eerdmans Publishing Company.
The reason why Judah is the holy place is because that is where the Temple is, in the land populated by the tribe of Judah. But Israel here does not refer to the norther kingdom, but rather to the entire community, as can be seen from the first verse:
When Israel went out from Egypt, the house of Jacob from a people of
a strange language,
Thus all the tribes are the dominion of God, and the land of Judah is the place where God dwells (in the temple).