Yes you need an employment contract.
No no no no no to the aupairworld.net contract.
What you want is the stuff from direct.gov.uk - here is a good starting point.
It can be very simple:
Your name, address (Mrs Bloggs, 1 AnyRoad, Anytown)
Au pairs name, address (Au pair, 5 AnotherRoad, AnotherTown, AnotherCountry, resident in the UK at 1 AnyRoad, AnyTown from 01/01/01)
Date contract starts, address where au pair works (01/01/01, 1 AnyRoad, Anytown)
Hour per week, pay per week (stated gross) and duties (1 hour per week, paid at £1 per week (gross) for X, Y, Z for our pet cat, Geoffrey)
Holiday entitlement - 5.6 week paid holiday which can include Bank Holidays, so equivalent to 4 weeks plus bank hols (5.6 weeks paid holiday per year to be chosen by the Bloggs family)
A sentence saying that the au pair is entitled to all statutory benefits which they accrue during their time here (aka none because they won't be earning enough)
Notice period, disciplinary procedure (verbal warning, written warning, dismissal) and cases for instant dismissal (gross misconduct) eg theft, neglecting, abusing or otherwise endangering the children, getting pissed on duty etc
IMO it's also worth writing in that you will be the au pair's primary employer in all circumstances, which means any other work she does is automatically her second job and she gets taxed/pays NI out of that.
You don't need to worry about pensions.
general info on employment
You are much better modifying a nanny contract (such as either from nannyjob) to suit you as it will cover the main employment points.