I think you'd have to be pretty close if you decided to follow
him to Singapore, so don't give up just like that. Like others have
correctly pointed out, you need to talk to him, tell him what's
bothering you.
It's only been 6 weeks - call it teething problems, whatever, just
give yourself some more time and try and acquaint yourself with
Singapore. It's important to find stuff that interests you here,
and perhaps a couple of friends, so that you don't feel so lonely
when he's busy at work.
