There are advantages and disadvantages to traveling with an infant on a plane or train. However, traveling on a plane may be best, because planes are generally faster than trains.
afraid to fly
Prefers train, but will fly if pushed
A bus or train or boat.
You can't take a train directly from the Shetland Islands to London. You can't even fly directly between Shetland and London. You could travel by boat from Shetland to Aberdeen and then take a train or fly from there to London or you could fly from Shetland to Edinburgh and either fly or take a train from Edinburgh to London.
You can't travel from Edinburgh to Belfast by train because Belfast is in Ireland which is an island. The easiest way is to fly.
Providing the infant has suitable documentation and supervision.
To be honest, it's probably better to fly, but if you want to take the train, you will need to take a train first from Barcelona to Venice in Italy. Then you will need to take the train from Venice to Vienna.
Travelling by train between Brisbane and Cairns is much more scenic, but of course it takes two full days, whereas the flight is just a couple of hours. Long-distance train travel is a truly unique experience, and preferable if you are wanting relaxing holiday travel. You see much more of the countryside than if you fly, and the stewards on board the train do everything they can to make your journey comfortable. If you choose to travel by train, ensure you book a sleeper cabin, and don't try the economy method.
Different airlines have different rules so check with the airline that you intend to fly with. The easiest way is to travel by train.
You cannot put tools in your carry-on luggage on an airplane. They may be in your checked luggage to fly, or if you travel by bus or train.
The best way to travel between Edinburgh and Aberdeen is train. You could also drive or take a coach.
Fly, drive, train, bus...and then you could always bike or walk.