Thanks everyone for the comments!
The "UA932 which arrives at 11:50, departing to VCE on LH328 at 12:50" is indeed the one we were looking at.
An alternative is UA 989, arriving 7:10 AM and departing 8:30 AM on UA 9078.
We came through Frankfurt in the summer on a flight from the UK. Immigration was very slow, but I didn't yet have my EU passport and so couldn't use the automatic gates the EU passport holders were using, which were very fast.