I’ve implemented FullCalendar and qTip together (not in Modx) before. It builds the interface using javascript, jquery.
You should be good creating the events list data using getResources Snippet.
Use a folder container for events and TVs for creating additional properties you’ll need for the events.
Once you have semantic html data events data listed in a page (or in a javacript object/array), jquery and fullcalendar can handle the rest.
Check this page’s source code were i’ve used FullCalendar in the "Calendario" section for a insight.
http://www.uepa.com/v5_eventos.aspx
Hope it helps.