Hello and welcome

Zoomie is such a great name! Assuming there are no issues between States (I'm not aware of such a thing) you'll need to think about the best way to travel. I'm pretty sure you can't take them on a flight (usually) and would probably need to drive - presumably that could be a 3 day journey? (I have no idea how long it takes to get from LA to New York by vehicle!). Maybe hiring a motorhome would be an idea. - If you can pack all your stuff on top of it and have a kind of home from home for the journey. Then you and your hamster would be in a kind of normal living environment in the evenings. during the days the hamster would need to be in a pet carrier, wedged in somewhere - so it couldn't get thrown if you had to brake eg. It wouldn't be safe to leave them in a cage while driving. But you could have a holiday cage set up in the campervan so when you stop at night, the hamster could go in the cage and have some interaction with you in the evenings. You'd also need breaks during the day to check on the hamster and make sure they have water and food (although they do tend to sleep all day so mainly cucumber and water accessible). And allow plenty of time for the journey with overnight stops for some normality.
I think providing you're around at night and they have a cage with familiar smelling bedding and toys in, in the evening, the hamster would manage this fairly well. The stability would be the home environment with you.
Can you give us more info on the drive journey time?