While there are no certainties, holrs514 and you could be unlucky (such as repairs on an A388 being suddenly required, delaying departure), the good news is that the delay to QF8 that arrives tomorrow morning (Tuesday 11 July) should not of itself affect any QF A388 departures.
The bad news is that if something goes wrong, from looking at timetables after the departure from DFW at a scheduled 1435 hours for AA1348, the remaining two AA flights from DFW to MSP are timetabled to depart at 1835 and 2030 hours, so they are not evenly spaced and you would potentially face a lengthy wait.
Be assured that QF7 typically has a better timekeeping record than the Oz - LAX A388 or B744 QF flights, although if anything the worst performers tend to be the westbounds back to Oz, in no small part due to the connecting JFK - LAX QF12 that to put it nicely has a variable timekeeping record. QF8 is unaffected by all that, so again it is quite unusual for it to arrive significantly late. Frequent QF users may be aware of this with the other factor being a desire of some to avoid LAX (although my most recent experience last year was very pleasant: I found it efficient and even the immigration officer could not have been more courteous.)