I thought 子供 just means child?
Your understanding is correct. 子供 (child; kid) is a gender free term.
Please see the sentence source. 子供がベッドから落ちた in Japanese, sourced from Tanaka Corpus, are linked to two different English versions:
The boy fell off the bed. (ID: 245655, sourced from Tanaka Corpus; the current Clozemaster version)
The child fell out of bed. (ID: 508836, initially posted as a translation from Spanish and later linked to Japanese)