東京からニューヨークに行くのだけど、一回ダラスで乗り継ぎをしなければならないって英語でなんて言うの？

"Stopover" and "transit" are very common words to use in this case.

Stopover = a break in a journey. "I have a brief stopover at Shannon Airport" synonyms: stay, stop, break, stop-off, visit; formalsojourn "She has a 2 hour stopover in the United Kingdom en route to the US" Via = travelling through (a place) en route to a destination. "They came to Europe via Turkey"

On my trip to New York from Tokyo, I'll have a stopover in Dallas. A "stopover' is a break in the journey. The word "stop-off" is another word for stopover.

So, normally you can use layover (long) or stopover (brief) depending on the duration of transit. However, Americans are more familiar with the term layover, and we can sometimes use it interchangeably to describe a brief or long stop en route from our departure to our destination. You may also hear some people say that they have a connecting flight in one city; i.e. "I'm flying from Tokyo to New York, but I have a connecting flight in Dallas."

The term I always use (and hear used by friends) for connecting flights is, "layover" which means no explanation is needed. In the second sentence, I explain that the flight is "not direct" which means that I have to get off one plane and get on another to reach my destination. In the third sentence, I make it clear that the final destination is not Dallas, but New York by use of the phrase, "connecting flight."

You can say: I am travelling from Tokyo to New York with a stopover in Dallas. You have used the verb 'travelling' in its present participle tense because the travelling is continuous. However, there will be a stopover in Dallas. 'Stopover in this context means 'to stay at a place for a short period of time on the way to somewhere else'.

These sentences will tell someone that you have a connecting flight in Dallas on your way to New York from Tokyo.