Honestly, this could be tough. While Singapore is generally dog-tolerant, Islam teaches the Muslims (about 10-20% of the population) that dogs are dirty and they (Muslims) have to clean themselves in a particular way if they inadvertently touch (or are touched by) a dog. This seems (just my theory) to have had a ripple effect for the rest of the population, so while no-one is hostile to dogs, they certainly aren't welcome in restaurants (I agree with that one!) nor most public transport.
Some taxis will accept dogs, but it's best when calling a taxi to tell them in advance, to avoid rejection when the taxi arrives. I don't know whether even the most tolerant taxi-driver will be happy about a big (!) dog, since ours is quite small.
I don't think dogs normally need muzzles, but except for a couple of designated 'dog parks' all dogs have to be on a lead when they're on public
property.
Sorry I couldn't give you better news. Good luck.