Cat is not a problem as above poster mentions depends on your circumstances when you arrive, we had 2 weeks before we got our own place - so we used Par air services they ship RAF sniffer dogs to earthquake places. They put the cat in their cattery for a couple of weeks before shipping him over (cost around 600 pounds). No quarantine this side as no rabies in the UK. But you must keep up the rabies injections here to get your furry friend back. Have a look here for more info about the rules: http://www.ava.gov.sg/
Footy - not a problem, there are lots of sides, I would recommend the Pirates - good crowd of blokes. He might be grateful to be in goal as it is very hot & humid here to be running around. Send me a PM & I can get you in touch with them.
For yourself I would say settle down first here & get a feel for the place, I know you like to keep busy, but moving countries you will find yourself very busy initially. Depending on the type of pass you have decides whether you can work on not, with your other half's $ you could become the typical expat wife or if you want something more worthwhile get involved in charity work.
Good luck & hope you like it here
Ahh just re read your post one thing - as you are not married you do not get a dependancy pass so you will only have 1 month visa when you arrive here. You can get a letter from a solicitor to say that you are dependant on him, or you can get a social visitors 6 month visa, requires a deposit or local reference. If you can't find a job before you get here it gets harder when you are here. What I did was set up my own company & that got me my visa, then found work after a while but it is not easy as most jobs are offered to local or PR (permanaent residents).
That may be your biggest hurdle - my advice is look for a job in Singapore from Scotland or at least line up a few interviews.
"An intelligent man is sometimes forced to be drunk to spend time with his fools."