Do it. My sister has so many kids and such a busy schedule, that their parties are often the month before or after their birthdays. It's really common.
Do it. We did E's 2 weeks early because he was having surgery 4 days before his birthday and I wanted him to be able to enjoy some cake instead of doing it 3 weeks late and maybe not healed completely from surgery.
Absolutely. One thing, though. I had DS's 1st b-day a week early. It felt weird! I felt weird singing to him, etc, and it wasn't REALLY his birthday. It's just a mental thing, and I wouldn't let it stop you. But just be prepared.