There's generally a HUGE drop in appetite that happens around 1 yr of age. Babies and toddlers have an innate ability to regulate their appetites based on what their bodies need, so unless she seems ill, is losing weight, or waking from hunger during the night, I'd imagine that's what's going on. My DS can literally live for days on nothing but air, only to eat me out of house and home a few days later. Also, choices can help, even if she isn't very verbal yet. You can hold up 2 foods and ask her to point to which one she wants, and that might help her get more interested in eating.
Is she in a high chair? 13 mo seems a bit young to expect her to sit down on her own and eat, they generally need to be contained for a few more months. If you'd like for her to stop grazing, your best bet is to stop offering food on the go. Most toddlers her age eat 3 meals and 2 snacks a day (we do more on hungry days). When it's time to eat, sit at the table with her and offer her food. If she chooses not to eat, end the meal without making a big deal out of it. Then wait until the next meal or snack to try again. It might be rough, as she'll likely get hungry earlier, but you gotta stick with it if you really want to break the habit!