kdoner,
At this point in your career, Singapore, and almost all the other large-cabin, wide-body airlines, are still a bit out of reach.
However, it's never too early to begin doing legitimate research and mapping out potential career plans. BUT, I'm sure you've noticed that pilots' careers rarely go the way they were planned. Keep working, keep looking, and if you're open to travel, look to developing third-world nations with regional aircraft and narrow-body jets. Upgrades may be quicker, but the QOL may be lower.
Everything depends on your personal pain threshold. Best wishes!
Viliamu