Filter a django QuerySet with the query from another QuerySet: Possible?

Say I create a QuerySet like:

q0  = Thing.objects.all()
fq0 = q0.filter(x=y)

at time t0. Then I add some new things to Thing db. These things form the QuerySet:

q1 = Thing.objects.filter(created_gt=t0)

I want to generate the QuerySet:

fq = (q0 | q1).filter(x=y)

Without having to know what x or y are. In other words, i'd like to be able to do something like this:

fq1 = q1.filter(query=fq0.query)
fq = fq0 | fq1

Is this possible? Manually setting

q1.query = fq0.query

merely sets q1 == fq0. I've seen some people asking about extracting the sql from a queryset, but this won't really help me.