I'm more inclined to agree with [SingerOfTheFall's answer][1].  
Upon Gaara's birth (*Shipuuden* episode 297 and *Naruto* chapter 547, page 4), he already had his dark rings around the eyes.  

<img src="http://i.imgur.com/3Wdfu8E.jpg" width="428" height="408">

I know he already had the Shukaku sealed inside him, but I find it a bit odd that he was born suffering from insomnia.  
Plus, the translation I read of chapter 135 does not refer to the dark rings, but rather to the 'bags under his eyes' (although this could be a problem with the translation...):  

<img src="http://i.imgur.com/yKcxreo.jpg" width="304" height="466">  

Furthermore, as SingerOfTheFall said, there are several other Suna shinobi that have dark rings around their eyes, including [Gaara's father when he uses his Gold Dust][2]:  

<img src="http://i.imgur.com/9i6G1oO.jpg" width="382" height="216">  

-----
On a side note, I think it can also be the influence of the tanuki ([the 'inspiration' for the Shukaku][3]) in the character conception, since the tanuki too has dark rings around his eyes.  

<img src="http://i.imgur.com/ihJX349.jpg" width="408" height="272">  

So this trait could be somewhat similar to the whiskers Naruto has from the Kyuubi. He had these whiskers even prior to being the Kyuubi's host:  

<img src="http://i.imgur.com/f4dOcIE.png" width="540" height="304">  

This could mean that the dark circles are a character trait (conceived upon character design) that were a result of the Ichibi being sealed in Gaara even before his birth, thus being present even after the Bijuu's extraction.


[1]: https://anime.stackexchange.com/a/1951/49
[2]: http://naruto.wikia.com/wiki/Fourth_Kazekage#Appearance
[3]: https://anime.stackexchange.com/a/795/49