Again, sorry!
On a practical note, what you could do for a quick n' dirty approach is:
1. Buffer your point layers (a buffer for each point) to the desired distance
2. Run a point in polygon (Vector->Analysis Tools -> Points in Polygon) count using the resulting buffer layer - this will give you a new file with a column called PNTCNT - this is the count of points within the buffer radius first set.
Depending on how complex your point layer is, the second step can take a few minutes to run.... so you'll have to be patient!
I recently used this process to produce this map (
https://flic.kr/p/o8FaNk), it took about 5 minutes to run the point in polygon count with approximately 10,000 points .
Cheers,
Andy