Your almost done, all that's left is to change to the new boot environment. This is a simple command followed by a reboot, and the point at which your only downtime occurs.
# beadm activate 10.1-RELEASE-p3-r276159-2015.01.09 Activated successfully
I like to follow this up with a beadm list to verify everything before rebooting.
# beadm list BE Active Mountpoint Space Created install N / 875.6M 2015-01-02 13:56 10.1-RELEASE-p3-r276159-2015.01.09 R - 1.7G 2015-01-09 12:13
Note: The Active Column is key here, it shows that currently the install boot environment is active, and that the new environment, 10.1-RELEASE-p3-r276159-2015.01.09, will be activated at reboot.
Reboot and Done.
shutdown -r now
Note: of course you should verify that everything is functional after the reboot.