I think that you should not be afraid of "how much memory do QStrings consume" but of the fact that your char* stuff is a pain to be maintained.
It's a simple calculation. Now you have roughly 240 kB after init. With QString pointers, let's say ten times or twenty times as much - I do not have the class declaration at hand, sorry. So you'll end up with a memory consumption of less than 5 MB compared to the 240 kB before. From my point of view there is no system running with C++ libraries that cannot spend additional 5 MB.
Go for it, you'll love string handling and you will ask yourself how you did things without. At least, if you mind the QString class, use std::string. Both string classes can be resized, searched for other strings etc. without big effort.
There are 10 types of people in the world. Those that understand binary numbers and those that don't.