I'm reading your question about the camera, but I'm also reading why you want this (to image Jupiter).
First, to address your direct question on vibration with the 1200D:
The 1200D lacks "mirror lock-up" mode. This is the traditional way to eliminate vibrations caused by mirror-slap. You would have to use live-view mode to eliminate mirror-slap with this camera.
Next, to address planetary imaging:
However, imaging planets is very different from imaging deep-sky objects (DSOs). DSOs (nebulae, galaxies, etc.) are normally imaged via many long-exposure images which are stacked. Planets use a form of "lucky imaging" in which you capture many frames of video, parse through to find the best frames, and then stack those.
This means that to get good results on planets, you would use video instead of single frames. Ideally this would be uncompressed video frames. The camera should preferably be capable of at least 60 frames per second. And because it's Jupiter (which rotates much faster than any other planet in the solar system) the upper-limit for capture time is about 1 minute worth of data (going beyond that will result in the stacked frames blurring from the rotation -- although there is de-rotation software as WinJupos which does a bit of magic with the images to re-map the pixels for better alignment).
The top planetary imagers are guys like Damian Peach and Christopher Go. Damian has a chapter in the book Lessons by the Masters which details the process.
Check out images at Astrobin (extremely popular website for posting astrophotography): https://www.astrobin.com/search/?q=Jupiter&d=i&t=all
Most astro-imagers post details including equipment used, software, and sometimes the processes. You'll notice that ZWO brand cameras are extremely popular for this sort of work (ZWO cameras have model numbers that begin with "ASI..." such as ASI290MC or ASI120MC-S). The least-expensive is the ASI120MC-S and it's able to capture at 60fps (higher end models are much faster). The trends in which cameras are popular changes over time (past brands have been QHY, Imaging Source, Point Grey, etc.) but you'll also notice if you browse through the best images that it's extremely hard to find anyone who uses a DSLR for this type of imaging.
Atmospheric seeing conditions will distort the image quality (picking a good night to image helps). This is where "lucky imaging" comes in. Software can help analyze the video frames and pick the best frames to stack ... rejecting the rest. AutoStakkert and Register are popular stacking programs (and free) for planetary image stacking (don't use these programs for DSOs).
You can use a DSLR for this (put the camera in video mode), but you'll find it easier to get good results with the dedicated CMOS astro-imaging cameras. (In US Dollars, an ASI120MC-S is around $150 ... which makes it a pretty affordable camera.)