You need to use an aggregation function to get the count before you can filter on it.
from django.db.models import Count
myObjects.filter(
links_by_source__status=ACCEPTED).annotate(link_count=Count('links_by_source')
).filter(link_count=1)
Note, you should pay attention to the order of the annotate and filter here: that query counts the number of ACCEPTED links, not sure if you want that or you want to check that the total count of all links is 1.