That's far too small for a filament printer, you are seeing micron details in that image. As SandervG says, the smallest nozzle is 0.25mm, so that gives the finest line possible with the Ultimaker.
Maybe with a 1.15mm nozzle but you need to be a very advanced user and even with that I don't think precision would be enough for your request
I think even with the smallest nozzle you are still dealing with melted plastics and pressure and extrusion and sticky lines so that size is probably too small..
Just buy a bigger microscope. That way you can print it a bigger size.
I have been playing around with 2D images and using cura to convert it to 3D. I would only recommend using images that don't have to many edges when it extrudes up as different dark or light colours will have different height values. And you will get a lot of stringing, which are almost impossible to clean up. A heat gun will also not work as you will just end up warping the object.
Also, even if you could print that small then I doubt you will be able to see what you need to see. You can just as well print out a single layer and cut it to size and put it under the microscope.
I would use a Form Labs SLA Printer id think that's your lot at that size...
Welcome to the forums!
You can load your jpg in Cura 15.4 and it will automatically open a window with settings on how you want to print that jpg-file.
However, I strongly think 1mm*1mm is smaller than what an Ultimaker can print.
You must understand that the nozzle you use to print is by default 0.4mm which is already half of the print you want to make. You can swap it to 0.25mm nozzle, but working with thermoplastics I don't think you can add the details you are looking for on a 1mm*1mm print.
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