Not sure if the Indian passport will be an issue. There's a Premier Inn attached to the airport but would mean going through passport control. Worth checking with them if they can do something for you

Alternatively there are paid individual sleeping pods but a toddler mightn't go for that. Love to know if anyone has tried them and if they are quiet and clean

Finally you can now pay for access to the Etihad lounges which may give a little respite but are bright and not conducive to sleep, they will be quite quiet for a while after 9AM though after that bank of European flights have left

Hope that helps