Aunty it is the simple things that will amuse your neice.
Remember the heat will probably get to her so plan for morning activities if outside.
Here are some ideas:
Some toy for the pool
Zoo
Birdpark
East Coast with the beach
The merlion
Wild Wild Wet (although you will be limited to where she can swim and what she can do)
The adventure park at Pasir Ris (next to wild wild wet) - again quite some limits on height
There is a book called Fun Singapore for kids - its cheap and has lots of ideas for kids
Also going out to McRitchie - not sure if the monkeys are hibernating from the heat at the moment but there's the turtles
The indoor play areas are a great idea as well - kids love rooms with balls etc
The playground at your condo - where she can interact with other children her age
What I tend to do is do some kids stuff and mix the adult things with that - as long as they can let out some of their steam they will tend to sleep in the pram while you do your things as well.
If you go out for dinner - take some colouring in books, toys that can keep her amused.
Hope some of this helps.