"We need at least an hour."
Μετάφραση:Χρειαζόμαστε τουλάχιστον μια ώρα.
There is no difference in meaning or stress in this case. Μία/Μια is just one of those words that can be pronounced both ways. Δύο/Δυο is another example. And because they are used interchangeably, you can find it either as "μία ώρα" or "μια ώρα", maybe depending on the personal preferences of whoever translated each sentence in the database. Being a team of different people, takes its toll on the consistency. :)
I may be wrong so wait for a real reply: but I think μία would place the stress on the ί whereas here the stress is on ώρα. Now I'm waiting for an official reply. Happy learning.