Starting school is common reason to catch repeat infections. They are mostly of viral nature and go off on their own. A good immunity like in adults takes time to develop which is by age 5-6 years. Till then children often show a kind of reaction to any new infection
But some children show a good resilience too. What can you do to make your child also very strong? First of all know that it will pass off making the child stronger every day. Protect her with all the needed vaccines esp the Influenza vaccine.
Take care of a good and healthy diet rich in proteins, vegetables and fruits. Milk/ paneer/ cheese/ curd must be encouraged. Usually they are fortified with
vitamin D
You are right about sun exposure. We all have started staying indoors. Put the child in some kind of sport training - outdoors always better. Could be a choice of the child. Swimming is an excellent skill to learn while exposing the child to sun too. The sun exposure should be preferable be before 10 am to avoid sun burn.
Screen time including TV or iPad to be less than 1 hour for her age. A moderate to vigorous exercise of at least 60 min daily - includes chasing, climbing, dancing, ball games or swimming and a total of 3 hours playing ( could be any light games). This too helps in keeping the child healthy and boosts immunity and strength. Brings discipline in the child, gives social skills
Lastly, your question - iron and vitamin d. Better to test first to know how much supplements should be taken. Till then you can safely give either of these - Essentuals plus - 1 ml daily or Ultra D3 drops 1 ml daily. First one has advantage of DHA in it.
For iron it is best to eat fruits like apple, pomegranate, dates, all dry fruits, green leafy vegetables. If taking them 1 egg every day, fish or chicken. And all kinds of whole grain dals.