I also take shots on Friday. I had a situation where I was traveling...flight on Thursday...shot day on Friday. Nurse allowed me to take my shot on Thursday before the flight...then the next week moved the shot back to Friday.
You should talk to your Dr's office.
Yes, you can move your shot to Thursday. Just make sure subsequent shots are taken on Thursday night. Moving shots to the next day after is not adviseable, but 1 day early is fine as long as you keep the same day.
Trinity