It's actually fairly outrageous that a camera of that supposed quality and cost does not have a mirror lock-up/control, however, I suspect there are plenty more. Personally, I have always viewed lock-up as vital in any SLR type of system, if only for peace of mind.
The answer is to use the cameras self-timer which is intended for getting yourself in the picture. Most DSLR's have both long and short duration timer. Usually the short one is 2 seconds and the mirror flips as soon as the shutter is pressed. This leaves nearly two seconds for any movement to cease before the shutter trips.
As with everything to do with photo gear, you need to test carefully before using on anything important.