Dogie comes from Spanish "Dogal," a motherless calf; an old vaquero term picked up by American cowboys.
According to Ramon F. Adams, during trail days, "when it was discovered that the northern range was good cow country, especially for fattening beef, there arose a demand for young animals. It became the usage to call them dogies, especially yearling steers, to distinguish them from steers that were fat enough for market."
The vaquero word, like many others, was picked up by the Anglo cowboys.

Adams also quotes the 'dough-guts' explanation, but the vaquero origin now seems to have the widest acceptance.
This has been explained in a couple of threads. For 'dogal,' see the excellent little booklet by Donald Gilbert y Chavez, published by the University of New Mexico, and put on the net. http://www.unm.edu/~gabbriel/index.html
Cowboys-Vaqueros
Go to Chapter 9, Lingo & Definitions.
Also see Ramon F. Adams, 1944(1956 revised), "Western Words," University of Oklahoma Press.