Yes Elder Price, the Mormon church still believes that you'll get your own planet

"I believe that God has a plan for all of us. I believe that plan involves me getting my own planet."

This is a quote from Elder Price in the "Book of Mormon" musical.

If you haven't heard the song that this quote it is taken from ("I Believe"), you should. It's a good and fair summary of Mormon belief.

Of course, it's also very funny, as are most Mormon beliefs.

But the LDS church isn't laughing; it's trying to find a way to tell non-Mormons that it doesn't teach the things that Elder Price believes, yet do it in a way that won't upset Elder Price and other Mormon believers too much. That's a difficult task, but judging from the news articles that reported on the LDS church's latest attempt, they've managed to pull it off.

[See for example ABC News: No, People Don't Get Own Planets in Afterlife Like in 'Book of Mormon', HuffingtonPost: Mormon Church Dispels Planet Afterlife Misconception Fostered By 'Book Of Mormon' Broadway Show, and The Wire: Mormons Don't Technically Get a Planet Once They Die, Say Mormons]

The article (Becoming LIke a God) on the official LDS website uses 3500 words to carefully dance around the topic it is trying hard to avoid -- which is, of course, Elder Price's belief that he will one day get his very own planet.

This is as close as it gets to addressing the topic:

Latter-day Saints’ doctrine of exaltation is often similarly reduced in media to a cartoonish image of people receiving their own planets.

Notice that the quote doesn't deny that the LDS doctrine of exaltation implies that people will receive their own planets. It just says that this belief has been made into a cartoonish idea in the media. And it has. Here, for example, is a cartoon that fully explains the LDS doctrine of exaltation.

And while I can't verify that all of the beliefs mentioned in the above cartoon are taught by the LDS church, I can verify that it still teaches Elder Price's planetary belief. (Or it did 15 years ago, anyway.)

And how do I know this? Well, in 1999 my wife attended a (for credit) LDS Seminary class at Idaho State University in 1999 call "Achieving a Celestial Marriage." It used a student manual with the same title, from which the below quotes were taken.

p.129
GOD WAS ONCE A MORTAL MAN

(1-2) He lived on an Earth like Our Own
"God himself was once as we are now, and is an exalted man, and sits enthroned in yonder heavens! That is the great secret. ..." (Smith, Teachings, p. 345.)

GOD IS NOW AN EXALTED MAN WITH POWERS OF ETERNAL INCREASE

(1-4) Our Father in Heaven Lives in an Exalted Marriage Relationship

p.132
(1-9) Celestial Marriage Makes It Possible for Us to Claim Or Mortal Children in Eternity As Well As to Propagate Ourselves Throughout Eternity
"[A]ll who attain to this glory will have the blessing of the continuation of the 'seeds' forever. ... [T]hey will have a posterity that will be as innumerable as the stars of heaven.

To become like him we must have all the powers of godhood; thus a man and his wife when glorified will have spirit children who eventually will go on an earth like this one.... We will become gods and have jurisdiction over worlds, and these worlds will be peopled by our own offspring. ..." (Smith, Doctrines of Salvation, 2:43-44, 48.) [My emphasis.]

(1-20) SUMMARY
As shown in this chapter, our Father in heaven was once a man as we are now ... he and our mother in heaven were empowered to give birth to spirit children.... We are those spirit children.

So don't worry, Elder Price. The LDS church still believes that you'll get that planet. (They just don't want to talk about it in front of the Gentiles.)