I just learned that ''I'm hungry'' is :
but can also be :
Onaka peko peko
I noticed that the ''peko peko'' was written in katakana.
Does it come from ''peckish'' ?
Does ぺこぺこ come from ''peckish''?
No. Its derivation is from purely Japanese roots.
ぺこぺこ is traced to texts from the
early 1900s late 1800s (thank you, snailcar!). Granted, that's late enough to be an English-inspired term.
However, let's look deeper. Notice that this starts with a //p//. Historically, all of the modern //h// (and the //ɸ// in ふ) came from earlier //p//. Then //p// reappeared in around the Muromachi period. And, in fact, the Kotobank page for ぺこぺこ with various dictionary data shows that ぺこぺこ is related to へこへこ. And へこへこ is older, appearing in texts from the 1770s when English had almost exactly zero influence on Japanese.
Also, Japanese reduplicated adverbs can often be analyzed based on one half of the reduplication. For ぺこぺこ, one half would be ぺこ, and if we consider へこへこ, one half would be へこ. From here, we find an immediate relation in 凹【へこ】む ("to buckle inwardly, to become hollow, to sink in"). This is pretty close to some of the other meanings of both へこへこ and ぺこぺこ -- and, in fact, the "hungry" sense for ぺこぺこ comes by extension from the idea of "my belly is caving in".
Please comment if the above does not answer your question.