I tried single quotes in your quoted string...it appears to work
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
int main ()
{
char *ca;
char queryStringSet[100];
char command[100];
strcpy (command, "export QUERY_STRING=");
strcpy (queryStringSet, "'a=1&b=2&c=3'");
strcat (command, queryStringSet);
printf ("command = %s\n", command);
system (command);
ca = getenv ("QUERY_STRING");
printf ("QUERY_STRING = %s\n", ca);
return 0;
}