Hi jacqui1238,
Thanks for posting. As I understand it, you may be seeing an error when you use Quick Start.
If you try the Quick Start transfer a second time, how does it work? Use Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch. Be sure to keep the devices near one another during the process, and make sure both are connected to an outlet power supply rather than a computer to see if that helps.
If it doesn't, you might also be able to back up your older iPhone and then restore that backup from either iCloud or iTunes. This will cover your options if you want to try this instead: Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch
Best wishes.