1. Vectorize your raster with Raster>Conversion>Polygonize.
 2. Then use the filed calculator and create a new field *area*: Function *Geometry* > $area
 3. Afterwards you can filter out the small polygons (right click on vector layer)
 4. Save the filtered layer to another vector layer.
 5. Rasterize the filtered vector layer (Raster>Conversion>Rasterize)