By the way that verse one starts out, you know immediately that Isaiah 12 is a continuation of Isaiah 11. But, the tone is very different, so you can see why it was made a separate chapter.
1 And in that day thou shalt say, I will give thanks unto thee, O Jehovah; for though thou wast angry with me, thine anger is turned away and thou comfortest me.
2 Behold, God is my salvation; I will trust, and will not be afraid; for Jehovah, even Jehovah, is my strength and song; and he is become my salvation.
3 Therefore with joy shall ye draw water out of the wells of salvation.
4 And in that day shall ye say, Give thanks unto Jehovah, call upon his name, declare his doings among the peoples, make mention that his name is exalted.
5 Sing unto Jehovah; for he hath done excellent things: let this be known in all the earth.
6 Cry aloud and shout, thou inhabitant of Zion; for great in the midst of thee is the Holy One of Israel.
When Israel accepts Jesus as her lord and savior, the joy and thankfulness will be truly incredible.
Furthermore, there is a command woven into this prophecy. When Israel is saved, they will be called to go out into the world and proclaim Jesus to the world.
Do we see something like this, elsewhere in the bible?
1 After his I saw four angels standing at the four corners of the earth, holding the four winds of the earth, that no wind should blow on the earth, or on the sea, or upon any tree.
2 And I saw another angel ascend from the sunrising, having the seal of the living God: and he cried with a great voice to the four angels to whom it was given to hurt the earth and the sea,
3 saying, Hurt not the earth, neither the sea, nor the trees, till we shall have sealed the servants of our God on their foreheads.
4 And I heard the number of them that were sealed, a hundred and forty and four thousand, sealed out of every tribe of the children of Israel:
5 Of the tribe of Judah were sealed twelve thousand: Of the tribe of Reuben twelve thousand; Of the tribe of Gad twelve thousand;
6 Of the tribe of Asher twelve thousand; Of the tribe of Naphtali twelve thousand; Of the tribe of Manasseh twelve thousand;
7 Of the tribe of Simeon twelve thousand; Of the tribe of Levi twelve thousand; Of the tribe of Issachar twelve thousand;
8 Of the tribe of Zebulun twelve thousand; Of the tribe of Joseph twelve thousand; Of the tribe of Benjamin were sealed twelve thousand.
Is Revelation 7:1-8 a fulfillment of Isaiah 12?
I am reluctant to say, so. Although, I can say that they really do appear to be the same.
I think that we need to be careful about drawing connections between prophecies just because there appear to be similarities.