Speech foundation models (SFMs) have achieved state-of-the-art results for various speech tasks in supervised (e.g. Whisper) or self-supervised systems (e.g. WavLM). However, the performance of SFMs for child ASR has not been systematically studied. In addition, there is no benchmark for child ASR with standard evaluations, making the comparisons of novel ideas difficult. In this paper, we initiate and present a comprehensive benchmark on several child speech databases based on various SFMs (Whisper, Wav2vec2.0, HuBERT, and WavLM). Moreover, we investigate finetuning strategies by comparing various data augmentation and parameter-efficient finetuning (PEFT) methods. We observe that the behaviors of these methods are different when the model size increases. For example, PEFT matches the performance of full finetuning for large models but worse for small models. To stabilize finetuning using augmented data, we propose a perturbation invariant finetuning (PIF) loss as a regularization.