As I see it, your main issue is the time-scale... as you are looking for a nanny to start in probably less than 8 weeks time.
First look on Leeds Gumtree: Nanny - Work Wanted and Leeds Gumtree: Nanny Jobs (as some nannies post there by mistake). You can also put your own ad in that section.
Looking at Nanny Job adverts at NannyJob: West Yorkshire, Live-Out may help give you some idea of what jobs are on offer in the area, thus help you with deciding how much salary to pay. You can also place an advert on NannyJob.
Consider if you will accept a nanny who brings their own child... if you will, then state that in any advert you place.
You can also register with agencies... most won't charge you until you accept a nanny they send. However do check terms and conditions carefully.
Also consider local advertising opportunities - such as local newsagent, community centre that kind of place (anywhere which will accept a postcard sized advert for a small fee).
You may find that you can find someone who would not mind doing cleaning/housework for part of the day prior to collecting your DS from nursery. However nannies generally expect to be mostly doing childcare, so if you advertise it as a nanny position, then expect them to only be doing childcare. However you can ask applicants if they would want to do more hours doing cleaning & ironing.
When you say, collect from nursery - at what time of day would that be? Be very clear in any advert as to the persons likely working hours, as that can help applicants see if your job will fit around their existing commitments.
Remember to agree a GROSS salary, not NET as any applicant is likely to have other work/income thus may get no personal tax allowance allocated to your job. If you are not already aware of how to go about doing the PAYE - HMRC: PAYE Intro is a good starting point.