We did this very journey not very long ago. It worked for us as we were then travelling by rd the next day onto Malacca.
Due to some flight changes - KLM cancelled our 2130 flight from DPS to SIN and put us on SQ which was delayed so we lobbed into Changi at 0100. While we had a driver booked , who was expecting us at Terminal 1, I updated via email but when we landed and cleared at Terminal 3 there was no driver, so we jumped into a taxi.
Now a Singapore taxi cannot take you across the border so the process is this. Get a taxi to the Queen st Taxi Depot - where you transfer to a car for the border crossing. We paid $25 or so SIN $ for the taxi ride then $38 SIN for the ride across the border.
Its very easy - you stay in the car - you hand your passports to the driver with your arrival card - at the border post the border guard - checks you by shining a light on you - with the window open, your passports are then returned to you - you next stop is Malaysian customs where you are asked a couple of questions and then you are in Malaysia.
We landed at 0100 and we were in our room at the Doubletree by Hilton at 0230 am.
I would not choose to stay in JB if Singapore is your destination - but if you want to be in JB or are doing onward travel in Malaysia its a great option.
We chose the DT because of the points - which were very low - and we thought the border crossing would be faster in the early morning that on a Sunday morning - and that was how it was.