How to transport my current marine life into a larger set up?

Yes you can transfer everything over to your new tank. I did it with a 55 gal to a 75 gal in one day. Take all your water out save it, then take out your gravel put in new tank, put back live rock in new tank and so on. you may have to add some new salt water but that will be fine. I added fish back the same all are doing fine.