This paper explores building a baby language model for Arabic in the context of the BabyLM challenge, with a pretraining corpus limited to 10 million words. We focus on two areas: 1. morphologically-aware segmentation and tokenisation methods suitable for Arabic, and 2. the unique challenges of data curation in diglossic linguistic settings, where the language spoken at home and in everyday communication (Dialectal Arabic) differs substantially from the written language used in formal education and most media (Modern Standard Arabic). We evaluate our models using the BabyBabelLM evaluation pipeline. We achieved a significant improvement in the grammaticality scores using different tokenisation and data composition strategies. We discuss these improvements in detail, especially what they reveal about the effect of mixing Modern Standard Arabic and Dialectal Arabic in baby Arabic language models, as well as the challenges they pose for building developmentally plausible models in Arabic.