Baby born in Thailand to Foreigner Parents with Work Permits – Non immigrant o for baby?

Hello,
My girlfriend (Australian) and I (American) had a baby girl (has American passport) around 8 weeks ago, in Bangkok. We will leave Thailand for two weeks to go to Australia. We were going to apply for a non immigrant o visa for the baby in Australia but is expensive and a hassle. Both my and my girlfriend have work permits and non immigrant b status
We were hoping that we could just get her a visa exemption on arrival, then go to Chaeng Wattana within a week to get her a non immigrant o visa. Is this possible at Chaeng Wattana? I am uncertain if this needs to be done outside of Thailand or not. My work will sponsor her and we have her birth certificate, both Thai, English Translation, and the American one we received from US Embassy. Its hard to find exact information on this as most immigrant o questions are for life companions.
Thank You for your help.