Question
I planted a peach seed in a small pot and it sprouted. When it reached about 7" I replanted it into a much larger pot. The result is something a kin to a vine about 18" tall. It is spindly and needs complete support. There is a second branch much heavier at about the 5" mark. Also the leaves look like grape leaves. To answer your question: I used a fresh pot and new potting soil. Any suggestions?

Answer
Hi David,
Thanx for your question.  If you're growing the peach tree indoors, this is why it is spindly.  It requires direct sunlight for optimal growth.  It needs to be outside in the ground.  You can cut the growing tip off at the top of the sapling to encourage more side growth.  If the plant has leaves that look like grape leaves, it is not a peach tree.   Here is a photo of a peach leaf.

http://www.hort.purdue.edu/ext/senior/fruits/images/large/peachleaves.jpg

Your peach will require a lot of water in the hot desert.  You shouldn't have any trouble with the winter.  Your winters are not as cold as many peach-growing regions in the mid and northern U.S.  You may want to post a follow up to this with a photo of the plant.  

The bottom line is, the plant needs to be planted outdoors where it will get about 8 hours of direct sunlight.  Side dress it with well-composted cow manure.  I don't know what you have available there but the plant should get some kind of fertilizer once in the spring and then again in mid summer.  I hope this helps.
Tom