I was told by the nurse at the EPAU that if you have a scan that shows a heartbeat, you have 90% chance of going on to have a healthy baby, whether the scan was before 12 weeks or not - I'm assuming she was correct. Our area do the "12 week" scan between 10-12 weeks now anyway.
Personally, I would say to tell people if you feel comfortable doing so, as nickelbabe says. I have done this each time - just told a few people close to me, and people that needed to know (e.g. personal trainer, hairdresser to check colour was OK to use, etc).
If you can afford the scan and would like one, I don't see any harm in having one. If it means you can't afford other stuff you really need, then no maybe it isn't the right thing to do.
If, alternatively, you want to keep it to yourself until later from personal preference, then it is your own business and no-one elses. I have spent my life as a non-drinker and yes people do seem to expect you to justify yourself for what is a personal choice! Make an excuse as Patagonia suggests above, if you don't want them to guess.
Other friends of mine have waited until having screening for Downs before telling, which made it later than 12 weeks. My best friend, who I've known for 32 years, didn't tell me till 16 weeks, as she had previously had a mc.
The 12 week thing is not the law, although it can feel like it, just do what feels right for you and ignore everyone else! :)