Upvote:2
I'm not sure where you saw you needed a cover letter for a UK visitor visa, not only is not mandatory document, it's not mentioned anywhere on the UK government website or their list of documents.
So no, you don't need a cover letter. However your kid does need a separate application and needs to mention one or both of you as accompanying adult on their application.
Upvote:3
Things work best when the consulate can 'link up' all the family members.
For a child you would use Part 7 "Travellers Under The Age of 18" and Part 9 "Remarks" of their application to include the parents' GWF numbers and/or passport numbers. It's fine to include the information in one of the parent's cover letter, but not as critical as identifying the relevant family members on the form itself.
More relevant information in this answer also.