Dogal in the sense of a motherless calf or a yearling could be Mexican Spanish. I only have the article my Gilbert y Chavez (he also gives the alternate meaning of a nose halter.
The general usage, regardless of origin, is for young animals; yearlings, as Ramon Adams says (see post above). Special handling cannot be afforded range cattle, especially on a drive.

The first time the word appeared in print was in 1888 in Central Magazine. It is in an inquiry by a farmer: "They were mostly Texas doughies- a name I have never seen written. it applies to young immigrant cattle." (OED). No indication of pronunciation, which depends on the syllable break- dou-ghies or dough-ies.

Adams, 1903, in his "Log of a Cowboy," p. 86, was the first real trail cowboy to use the word in print- "Before you could say Jack Robinson our dogies... were running in half a dozen different directions."
These obviously were animals able to eat the prairie grass, not little calfs needing special feeding.

"Dough-guts;" special treatment of this kind could only happen on a permanent site such as a fixed farm or ranch, but never on the trail.