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We'd rather be in a state within a state

I said that’s where we wanted to go to to my dog

“Z" is half of where I am. I’m called a wreath in another life. But now, I'm called exactly how I got here.

All my dreaming lead me here, no pot of gold at the end of this rainbow; though for the first time, its colors show

Reality is twice removed. Three ticks will get me half-way there

Do you know who I am?

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Mostly explained below, but I'm unsure about the second line now.

You are

DOROTHY GALE
Currently residing in Oz, wanting to return home

We'd rather be in a state within a state

From @EightAndAHalfTails: She'd rather be in KANSAS, whose letters are part of a different state, ARKANSAS

I said that’s where we wanted to go to to my dog

She sings about going "somewhere over the rainbow" to Toto (her dog)
I'm unsure about this line, because the clue sounds to me like she's in Oz telling Toto she wanted to go home (may have happened, can't recall), but my answer is her at home telling Toto she wants to go to Oz.

“Z" is half of where I am.

Z is half of OZ

I’m called a wreath in another life.

From @TwoBitOperation: Dorothy's actress is Judy Garland

But now, I'm called exactly how I got here.

Now she's Dorothy Gale, which relates to the twister that whisked her away to Oz

All my dreaming lead me here

It was all a dream...or was it?

no pot of gold at the end of this rainbow

Oz is "somewhere over the rainbow". While it has "yellow bricks" and an Emerald City, there are no pots of gold

though for the first time, its colors show

From @F1Krazy: When she arrives in Oz, the film goes from black-and-white to technicolor.

Reality is twice removed.

From @EightAndAHalfTails: Our reality -> Kansas/"home" inside the film -> Oz/dream

Three ticks will get me half-way there

To get home, she has to click her heels AND say "There's no place like home" three times

Do you know who I am?

Dorothy Gale

Also

First letter of each line = WIZARD

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    $\begingroup$ I think this is most certainly the answer. Perhaps the first line is rot13(Ersrerapvat Zhapuxva ynaq, juvpu vf va gur ynaq bs BM?) $\endgroup$ – Joe-You-Know Jun 8 '18 at 13:56
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    $\begingroup$ And the wreath line works because rot13: Gur npgerff'f anzr jnf Whql 'Tneynaq' $\endgroup$ – TwoBitOperation Jun 8 '18 at 14:01
  • $\begingroup$ @Joe-You-Know That could be it. Thanks, I've added it in. $\endgroup$ – hagfy Jun 8 '18 at 14:12
  • $\begingroup$ @TwoBitOperation Ahh, yeah, that definitely fits. Thank you. $\endgroup$ – hagfy Jun 8 '18 at 14:13
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    $\begingroup$ "Though for the first time, its colours show" - Rot13: Nsgre Qbebgul neevirf va Bm, gur svyz genafvgvbaf sebz oynpx-naq-juvgr gb Grpuavpbybe. $\endgroup$ – F1Krazy Jun 8 '18 at 14:13
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Partial answers that hagfy missed:

We'd rather be in a state within a state

She'd rather be in Kansas, which is a US state 'within' another US state, ArKANSAS

Reality is twice removed. Three ticks will get me half-way there

Even after returning to Kansas, she's not in reality (our world); she's in the film "The Wizard of Oz"

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    $\begingroup$ These seem good, so I've added them to my answer. Thanks! $\endgroup$ – hagfy Jun 8 '18 at 15:31

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