Just got back from there. If you need to rent gear, your best (and possibly only bet) will be to make the 3-4 hour drive north of Reykjavik to Viking Rafting (https://vikingrafting.is/
). They can set you up with full kit (boat/paddle/skirt/drysuit/booties) and shuttle for same price as they charge for a seat in a raft if you tag along with one of their commercial trips. It's more expensive than in the US, but then everything in Iceland is. They'll also set you up with gear and beta for running the shit, if that's your thing. The kayaks they have are river runners and creek boats - Burn, Mamba, Bazooka, etc. We brought our own PFDs, helmets, and pogies/gloves, so I don't know what that rental gear would have been like. The rafting drysuits they put us in were perfectly fine - rear entry with latex socks. Booties were NRS ATB Wetshoes.
You have two options if you decide to follow a commercial trip: class 2+ West Glacier River or class 4+ East Glacier River. My son and I did the West, since the videos of the East I could find made it look big, pushy, tight, and steep, and that's out of our league.
The West was an easy float, but it ranks up there as some of the prettiest and most enjoyable mild whitewater I've been on - 4.5 miles of continuous class 2+ with lots of dynamic eddies to link and basically no pools. In many places, the canyon walls rise straight out of the water on both sides. There are two good surf spots with eddy service, and a hot spring on the RR bank that's clean enough to make tea/coffee/hot chocolate with. After the confluence with the East, the water gets big and powerful. Rapids remain easy in that section, but be prepared for western-style 90 degree turns with big seams, eddy fences, boils and whirlpools.
Don't know what usage will be like in September, but we had the river to ourselves. The commercial trip we joined consisted of a single customer in a tandem IK with the lead guide.
I forgot my waterproof camera, so the only photos are what my daughter took from the road before the river entered the gorge section: