Good advice from tortoise.
You can't get them to eat if they don't want to. Imagine how unpleasant it would be for someone to try to make you eat when you are not hungry or don't like the food. And in my experience, once they work out it's a real issue for you, it can open a can of worms in terms of their anxiety levels and 'manipulating' and 'attention seeking' behaviour at mealtimes.
My nineteen month old sounds like tortoise's (and a bit like your's). She's dinky (dinkier than yours, I bet!) and always has been, but she's also energetic and healthy. Sometimes she eats like a horse, other times she seems to live on air. She's not especially keen on several vegetables, quite likes fruit. We eat together, I make sure that DD is prestented with a plate of varied, healthy and tasty food and then get on with enjoying my own meal. We talk and have a giggle, but it's not about how much we are eating/not eating. Before, when I gave her a separate 'tea' to myself an DH, she tended to perform and eat poorly. She always eats better when we are eating the same food as her and often tries something if she sees us eating it (even if it then gets spat out!). DD is also at the stage where she loves preparing food to eat (and quite a bit goes in during the preparation too!)
So, I've not got any advice about getting her to eat, just about enjoying mealtimes together and making sure that the food she does eat is healthy and varied (and I do go for a multivitimim syrup, just in case, although my GP said it is pointless -will just give her vitimim-filled wee!)