Hi Kate,
Space Mountain is one of my all time favorite rides! It is a very different ride the Pirates of the Caribbean where the ride vehicle is a boat. Space Mountain is a roller coaster in complete darkness.
Once upon a time, the ride vehicles in Space Mountain were designed where 2 people sat together in one seat. The larger of the two sat down first, was seat belted in and then the smallest person sat between his/her legs & another seat belt was put on. That has changed - now 3 people sit in one of the two connected ride vehicles so there is 6 total. Everyone sits in individual seats behind each other and only one person is allowed in each seat. You could put your DD in front of you but that is as close as you'll get. Space Mountain has was refurbished last year & the ride itself is even darker than before.
There is a minimum height requirement of 44" to ride Space Mountain. Keep in mind that just because a child is tall enough to ride a ride, doesn't mean that it is appropriate at the first age they meet the height requirements. Height requirements are set keeping safety purposes in mind.
I've had parents tell me that they've taken their 6 year olds on Space Mountain and they loved it - others were terrified. I don't think my 5 year old would be ready but you know your DD better than anyone & she may be a thrill seeker. Explain to her that it will be super dark, you can't sit with her, it has many twists, turns and small hills but no huge hills or loops. If you think she's ready go for it. If she gets in & sees the ride vehicles & wants to back out, there's always an escape hatch for those space travelers that want to abort the mission.
Let me know if you need more details. I am happy to assist you! Wishing you magical memories :-)