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Speech foundation models (SFMs) have achieved state-of- the-art results for various speech tasks in supervised (e.g. Whis- per) or self-supervised systems (e.g. WavLM). However, the performance of SFMs for child ASR has not been systemati- cally 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 compre- hensive 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 meth- ods are different when the model size increases. For example, PEFT matches the performance of full finetuning for large mod- els but worse for small models. To stabilize finetuning using augmented data, we propose a perturbation invariant finetuning (PIF) loss as a regularization.