Kismet bith my girls far preferred drinking to eating at around that age. Lucy went through a long period of having an Up & Go for morning tea which is pretty filling. I used to also make a lot of fruit and vegetable juices as Lucy also wasn't a fruit eater until she got older. The added benefit is it's a lot less messy than eating food around the house.
I used to refuse to let the kids walk around eating but at times if it's the only way they'll eat what can you do? Once she's back to her usual self then impose more structure on how she eats.