I would suggest that you properly repair the plasterboard. There are plenty of questions here and advice on the interwebz in general about how to do so.
Then, since your repair will likely lead you to finding the studs behind the plasterboard, I'd recommend that when you rehang the curtain rod, you bypass the rawl plugs/mollys/toggle bolts entirely by mounting the hangar brackets with longer screws that go directly into studs. Since it seems your poles go well beyond the window, there's nothing that will prevent you from having the hangars in from the ends so they do go into wood, it just means that you can't open the curtains all the way to expose the wall beside the window (you don't really want to do that anyway, do you?).
As an added bonus to the proper repair method, when you move out at the end of your lease you won't lose your damage deposit and/or when you go to sell, you'll really need to have this fixed up for the home inspection anyway.