HTTP.jl only adds the Content-Type automatically for POST: https://github.com/JuliaWeb/HTTP.jl/blob/255a75907a06b1340e7deac659383f15f3aa55f0/src/MessageRequest.jl#L58-L61.
I added that code but didn’t know if it made sense for any other request types. You can probably make a PR and relax that to POST or PUT at least.