If you are in Doha, better you continue here. Singapore started with the point system & they are no more attracting expat workforce, unless someone is exceptionally talented or qualified.
If you still plan to enter on a visit visa, make sure you stay there for atleast 2 months to get into your area of expertise.
The cheapest lodge will cost you a petty 15 SGD per night at Bencoolen (well connected with all areas of Singapore).

All the best..