Can she tie her own shoes and easily button small buttons (like a button down shirt)? If so, go for it, if not, I'd say it's a no go for now. That's about the level of dexterity I'd say it takes to do without frustration.
My son got a Rainbow Loom for his 8th birthday and love it, but watching him I doubt he could have done it very successfully even two years ago.
As pps have mentioned, you can make the bracelets with no loom just your fingers which is a bit easier... a 4 that might still be tricky, but you won't be out the saved allowance money... just the price of a bag of rubber bands.
Choose something that says 4+ for the age suggestion and she's be a lot happier!