I created your env. in my lab (calendar lists based on native SP calendar list template and the CAML filter to filter the events based on today's date) and everythong worked fine.
and be sure that thei match with the columsn required by qCalendar web part (Begin Date, end Date, Reccurence amd Title).
Let's make a quick test please. Create a new list based on the clendar template, create a new page, drop qCalendar on that new created page and link it to the new created calendar list. Create a few events then display the data. If everythoing works well add the CAML filter.