Thanks for all your replies!
PK99 - thanks very much but i'm a little bit far away in deepest darkest Dorset!
Am now facing another problem regarding this - my ex is saying he doesn't want our daughter going on the roads on a bike as its far too dangerous! Wish i'd never told him now! think will just go ahead and buy it.
You could mention that drivers tend to behave much better around cyclists with bike seats, trailers or tagalongs. There are idiots, but you'll get much more room riding something a bit out of the ordinary. Bung a flag on it for extra impact.
Also, your daughter will be much better in the long run, getting out in the fresh air, getting exercise, than cooped up in a car. And I suspect far more children are injured in cars, or just in the home, than on bikes. (there will be stats about that somewhere...)
As I assume you already cycle, your ex isn't bothered about you being on the roads? He may be your ex, but you're his daughter's mum, so he ought to care in that respect. You're probably safer with her on a tagalong as well - see my first point.
If it's possible, try one out with your daughter to see if she enjoys it. Is there a country park or similar nearby that has family cycle hire? That sort of place often has trailerbikes to hire.