Illustrator is the easier option for this job.

1. Apply your threshold and reduce your resolution to the desired values in Photoshop. Take note of the size of your image in pixels (25 x 17 in your example).
2. Copy a flattened raster version of this image and paste it in Illustrator. Yes, it's tiny.
3. Select the object and choose Object > Create Object Mosaic.... In the dialog box, enter the original image's resolution under the 'Number of Tiles' values and click OK.
4. Enlarge the result a few hundreds of percents so sizes in step 6 become workable;
5. Ungroup the result;
6. Select all of the tiles and choose Effect > Convert to Shape > Ellipse... and choose an 'Absolute' size of eg. 1mm by 1mm.
7. Click OK and be happy.

Illustrator is the easier option for this job.

1. Apply your threshold and reduce your resolution to the desired values in Photoshop. Take note of the size of your image in pixels (25 x 17 in your example).
2. Copy a flattened raster version of this image and paste it in Illustrator. Yes, it's tiny.
3. Select the object and choose Object > Create Object Mosaic.... In the dialog box, enter the original image's resolution under the 'Number of Tiles' values and click OK.
4. Enlarge the result a few hundreds of percents so sizes in step 6 become workable;
5. Ungroup the result;
6. Select all of the tiles and choose Effect > Convert to Shape > Ellipse... and choose an 'Absolute' size of eg. 1mm by 1mm.
7. Click OK and be happy.

Do note that the resolution reduction and the threshold in Photoshop are optional. Any embedded (as opposed to placed) raster image can be converted into a mosaic right off the bat.

^{_{Credits go to user56... and their awesome answer to this question.}}