Dogs can lick for a variety of reasons. In most cases it is due to a behavior, either boredom or nervousness, in other cases the dog likes the taste as they are very oral in nature, and in rarer cases there is a deficiency in the diet. The fact that she is whining as well tells me it may be more of a behavior problem. If she were eating odd things such as dirt or rocks then I would be more concerned with a health issue.
At age nine she could also be going through some cognitive issues that seniors start to develop.
IF she does not seem to be in pain in any way, then I would not worry about it. The behavior can be changed by teaching the dog the command 'leave it' each time she goes to lick a non food item.
If she eats non food items , this is called pica and she should be checked by your vet.