Self-supervised techniques for learning speech representations have been shown to develop linguistic competence from exposure to speech without the need for human labels. In order to fully realize the potential of these approaches and further our understanding of how infants learn language, simulations must closely emulate real-life situations by training on developmentally plausible corpora and benchmarking against appropriate test sets. To this end, we propose a language-acquisition-friendly benchmark to probe spoken language models at the lexical and syntactic levels, both of which are compatible with the vocabulary typical of children's language experiences. This paper introduces the benchmark and summarizes a range of experiments showing its usefulness. In addition, we highlight two exciting challenges that need to be addressed for further progress: bridging the gap between text and speech and between clean speech and in-the-wild speech.