Hi Amanda!
A 6 yr old definitely should not need deodorant. The reason for needing deodorant in the first place is because once kids get to a certain age their hormones start pumping. It's the beginning of this that starts giving boys that manly "stink", and makes girls need it when they are doing physical activities.
With a 6 yr old, I would look at two things. Number 1, is she getting enough water? If she isn't getting enough plain water (no juice, no tea, no soda, etc.), then her body will have a hard time flushing out the toxins, and therefore creating that concentrated "stench". Many times, this is what causes stinky feet, too.
If her water intake is excellent, then I would seriuosly consider seeing a nutritionist. I would have her diet evaluated for any deficiencies she might have. If it's not something she's lacking, it may be something that needs to be *removed* from her diet.
Blessings,
D.