"Can I calibrate anything so that the monitor image and the printed image are of the same brightness?"
You can use the brightness/contrast on the monitor to make it as close as you can to the printout.
Generally making screen pictures look similar to printed pictures is a "holy grail" for some processes (textile manufacturers in particular).
It's not easy, and thousands are spent on professional equipment to help. Remember the two representations of colour are entirely different - Ink is a subtractive process - mix all the colours and you get black. Monitors are additive - mix all the colours and you get white (light). See here click here
Since you can't readily affect the printing, the best bet is to change monitor settings.
Bear in mind the printing will change massively depending on the paper - and also on the ink if you're in the habit of using ink from different non-Canon manufacturers.