Generally you have to book cargo ahead of time, as the pet space is limited. Yes, there is a space reserved for animals, but never forget it's still cargo. There is an element of risk.
Has your dog flown long haul before? If you need tips on 'flight training' just ask.
Honestly I do not know what would happen if you planned on carrying your pet in the cabin and she was refused at check-in due to size. I would guess - but this is only my own guess, based on nothing - that if there were still space available in cargo they would allow your dog to travel that way on your flight, assuming the crate met cargo specifications. (Many people planning on traveling in cabin use a soft sided crate, which absolutely would not be allowed in the cargo hold.)
However, there might not be available space, in which case you'd be left scrambling for a solution at the airport. Which might not end well.
If you know what airline you will fly contact them now - most have a group responsible for animal transportation. Find out specific requirement,s get allowable crate dimensions, ask about booking procedures. And get the response in writing!
FYI, there might be a limit of the number of pets allowed in cabin, so you should make sure you fully understand booking procedures, especially timing.
Hope all goes well with the family travel and settling into your next chapter.
ETA:
Just to be clear: Animal travel needs to be booked ahead of time, both cargo and in-cabin.
To give you an idea of what is involved, take a peek at the Swiss website's pages on pet travel:
https://www.swiss.com/ch/EN/prepare/...g-with-animals
https://www.swiss.com/ch/en/customer...als-travelling
Obviously each airline will have it's own requirements, I just linked the Swiss pages because they are a good starter to get you thinking about issues that might arise with your dog's travel.