In addition to the good advice above, go to your primary care doctor to get checked out. You will need a doctor's report if you develop any complications later, and to support insurance settlements to cover any medical treatments. You probably feel fine today, but it typically takes a day or two for whiplash problems to manifest. If you miss any work because of this, or take any prescriptions, save all of your documentation to prove it. The other side's insurance company will demand this before they pay you anything.
My wife was rear ended twice, and both times she developed whiplash problems after a couple of days had passed. It took almost a year for the symptoms to resolve from the last crash. Both were at <5 mph, one with her stopped at a traffic light and the other driving through town when a pedestrian stepped out in front of her car and the other driver was too close.
Settlements from the other insurance company are completely negotiable. If you don't like the deal they give you, tell them you're considering small claims court or some other remedy. The adjuster's job is to get to a settlement without going to court, which is expensive for the company to manage (and for you, too). There may be some other posters with better advice on how to negotiate that settlement, but my advice is to have a number you want for the other company to make the problem go away. $1500 for a fender bender sounds pretty typical, maybe on the low side.