You will want the axle loaded and yes you should do it one side at a time. When I changed mine the hardest parts were tourqing the bolt back down tight enough because I couldn't get the right angle, and re attaching the emergency brake line because some of the slack had been taken out of it. An extra set of hands really helps.
Also, zip ties are fine for attaching the brake line to the lca.
2015 Mustang GT Premium | MRT Catback