You may need to URL-encode the JSON, the HTTP protocol might not be happy with all the special characters in it.
Also note that the "RPC=" is not part of the JSON - that's a key that will contain the JSON data in the HTTP request.
json$="{"+chr(34)+"version"+chr(34)+": "+chr(34)+"1.0"+chr(34)+","+chr(34)+"proc"+chr(34)+": "+chr(34)+"GetPlantOverview"+chr(34)+","+chr(34)+"id"+chr(34)+": "+chr(34)+"1"+chr(34)+","+chr(34)+"format"+chr(34)+": "+chr(34)+"JSON"+chr(34)+"+chr(34)+"}"
data$ = "RPC=" + HTTPEncode(json$)
SendHTTPRequest("IPaddress", "rpc", data$)
You could also try sending it via GET rather than post, though POST seems like the better option:
json$="{"+chr(34)+"version"+chr(34)+": "+chr(34)+"1.0"+chr(34)+","+chr(34)+"proc"+chr(34)+": "+chr(34)+"GetPlantOverview"+chr(34)+","+chr(34)+"id"+chr(34)+": "+chr(34)+"1"+chr(34)+","+chr(34)+"format"+chr(34)+": "+chr(34)+"JSON"+chr(34)+"+chr(34)+"}"
data$ = "RPC=" + HTTPEncode(json$)
SendHTTPRequest("IPaddress", "rpc?" + data$)