Insurance for baby

Okay so I’m in a weird position where both my husband and I are both disabled veterans and receive free healthcare from the VA. The VA will not cover my baby (even having a monthly payment) because neither my husband and I are considered completely and permanently disabled. So we qualify for Arizona Children’s Health Insurance Program (CHIP) state free/discounted insurance but I’m thinking that might take a while to take affect. Should I just plan on buying a month worth of private insurance for her until we can get the cheaper one? Health insurance is so confusing to me because I’ve been blessed by the military and before that my parents. Any help appreciated. Thanks!