It depends on how people assign you tasks. If they just use the New/Task button, I don’t know of any easy way to see your availability. However, if you train assigners to only assign Tasks to you from your Calendar View, and to only assign tasks on days when you have nothing else assigned, then you could simply create a week-long task (with a Start and Stop date) and entitle it “Brittany booked up, working on Important Task”.
In general, Asana is not a great solution for resource & load balancing as the data is not granular enough. For instance, I can’t natively include expected hours for a task, or look to see how many hours anyone is booked per day or per week.