You'll need to create a successful backup with your old device that contains 1SE then restore your new device from that backup. You can do this with iCloud or iTunes. It's paramount that this backup contains 1 Second Everyday.
VERY IMPORTANT: Please keep in mind logging into iCloud isn't the same as an iCloud backup. 1SE is NOT saved in your iCloud account. Only basic data like notes, mail, and contacts are. You'll need to do a backup via iCloud or iTunes.
Here's where you can see if 1SE is in your backup:
Want a step by step guide on backing up correctly?
How to Backup with an iPhone using iTunes or iCloud
Want a step by step guide on restoring correctly?
TIP: It's very important you make sure 1SE and its data are being backed up! We have no control over this. Please reference the graphics below.
Right now we don't have our own backup and accounts. But we know the community needs this and are working hard on it.