Underweight child. One go). please help.

My daughter is 2.5years old but is stuck at 9.4kgs. Her birth weight was 2.65kgs. she is otherwise very active and doesn't fall sick often and in line with her milestones  but I'm concerned about her weight and general wellness and deficiencies.. She has two teeth broken due to decay and two other have fillings. She doesn't like to eat much at one go.. and is very very picky . Doesn't like veggies  and lentils at all. She likes fish, egg, chicken but that too depends on mood. She absolutely resents whole milk. She was lactose intolerant after birth, which resolved at around 9mo this age. I'm single handedly managing everything and have an elder son - so I'm not able to devote as much time and energy towards her eating habits as much as I should as I don't have any help. On a local paediatric suggestion, I have just started with Zincovit syr 2.5ml twice daily (he said 5ml once daily, but she vomits when I give 5ml at one go). Please help.