She said we can pre-book the seats a few days before the flight
You should be able to book them straight away.
At least if you booked direct with Singapore you can. Personally I'd stopover in Singapore for a day or two, small and compact, plenty to do, and breaks up the journey.
The Singapore Stopover Holiday can be good value, you get free entry to the Zoo, Bird Park, etc, discounted food and a decent hotel rate (though I'd compare with other rates, but note that getting into the Zoo etc. will cost you a fair few S$)
www.singaporeair.com/saa/en_UK/content/promo/ssh/index.jsp
If you are just on a short stopover, you might wish to do the free bus tour. This takes two hours, there are two different options, the more suitable one probably would be the one with the boat trip.