BTM isn't really very intense. Your 6yr old should be fine. My brother who is 4 went on it this summer when me were there so it really all depends on if they like rides. I would take them on Goofy's Barmstormer in Toon Town first to see how they handle it if they get scared i would think BTM would be to intense for them.
My DD rode it first when she was 4 (half an inch above the height requiremen). She absolutely loves roller coasters. I agree with the above poster - take your child on the Barnstormer first and see how he/she reacts to that.
I'm pretty sure it is three in the car on BTMRR. I took my DD's 4 and 6 on it a few times in a row they loved it so much. There are no big drops. The height requirement on BTMRR and Splash mountain were 40 inches and the DD 4 thought she had to be shorter than 40 and kept trying to make herself fit under the stick.
It was cute.
Yes, they checked her every single time.
They also loved Splash Mountain but that has a big drop.
We were there in December. My 3 1/2 year old rode it and was exactly 40 inches. He rode once during MVMCP and once during a day visit. The fast, jerkiness didn't scare him, but the loud clanking as you are climbing hills and the mine scene with the rocks shaking and making loud noises frightened him. He didn't cry, but he decided not to ride more than twice. Just be aware that there might be more than the roller-coaster effects that can be scary for a small child.
We took our four year old ds on Barnstormer and BTMRR. He hated Barnstormer because the seats were very uncomfortable, but he loved BTM. He was so disappointed when we went back last year and BTM was down for rehab.