There are kids-friendly shopping malls in Singapore. For one, Westgate has a toilet specially for kids. You could bring her to watch a movie over at JEM and let her use the toilet at Westgate.
Otherwise, you could let her use the ladies but do keep a close eye on her. Try to approach a mother with kids on her way to the ladies and ask if she can keep an eye on your daughter.
http://bumblebeemum.net/2015/05/28/top-5-kids-friendly-shopping-malls-in-singapore/
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