Is it a bad idea to move my PC around when my loop is complete?
No one seemed to answer this so I'll give it my best shot: It isn't bad. A couple things you have to make sure: tubing is secure and tight on the barbs or fittings. If you're worried about tubing coming loose/leaking, put some clamps for double protection. Better be safe than sorry. If you get a pump/res combo, then I would just make sure that the hole is tight enough so water doesn't get out during transportation.
And of course always leak test your rig before installing anything to ensure no damage in the future.
I did my first loop and transported to and from a LAN party that was 60 miles away in my car with no issues. Just gotta take proper precautions.