What makes you think she is not making enough saliva? Have you discussed this with the pediatrician? Is the doctor concerned about some medical issue that inhibits saliva? Whether she is chewing has to do with how many teeth she has and where they are, as well as the habit of breaking them up. But a lot of kids are "gumming" foods too.
How big are the pieces you are giving her? How much does she get at once? Usually people start with small pieces of soft or easily-dissolvable foods, and only give the child 1 or 2 at a time. Cheerios and bananas are very common first foods. Watermelon is almost all water. Usually doctors say not to give grapes and hot dogs - they are choking hazards even if cut. Berries would be a good choice, also pasta (the curly shapes are easier to pick up - rotini, for example). Small pieces of cheese, yogurt with soft fruit in it, small pieces of meatloaf that will break up easily, cooked zucchini, and well-cooked carrots are good starting points.
Try coaching her a little with the chewing, by doing it yourself. Make sure nobody is talking with food in their mouths (because, really, we all tend to do that a bit), model the right behavior by taking small bites, and then exaggerate the chewing motion while she does it too. Emphasize the taste and savoring of the food rather than the quantity. Try not to study her anxiously (and tell your husband not to) so she doesn't pick up on that stress, and just focus on the experience of eating together as a family, at the table, in a high chair, no running around. She'll get the hang of it.