This seems like a simple question, but there are many considerations. Let's assume that you are under 18.

Just running away by itself does not give the state reason enough to take away your baby. They must prove that you are unable or unwilling to parent your baby (or your "dependent child"). The bad part is that under Arizona law, you are a child until you reach the age of 18 yourself. If your parents can't parent you, because you are a chronic runaway or won't listen to them, you could be placed away from your parents (found to be a dependent child yourself). Sometimes dependent kids that have kids of their own are placed with special families or foster homes that are willing to take a child parenting a child.

The simple answer is "no", your baby can't be taken away from you if you run away from home. But you would have to show that you could take care of the baby, with adequate food, clothing, shelter, medical care and supervision. This could be very hard to do when you are under 18.

There are many community resources for teen parents.  For instance Child and Family Resources in many of Arizona's cities has parenting programs.  You can also call Community Information and Referral at 602-263-8856.