It could be the problem if the rattle comes when going over rough roads.
You can check the sway bar links yourself. They need replacing if they are completely broken or if the rubber boots are torn at all.
They only cost about $12 each and take about 20 minutes to replace both. They are easier to replace with the rear wheels off.
Here's a pic of one of my new sway bar links installed. I took this pic before I put the second "locking" nut on. My old ones had tears in all the rubber boots and had no grease left in the sockets.
