Could you try to meet some of these other local childminders and ask them about how much demand for childcare there is in the area.
Could you ask your local authority Family Information Service for a current vacancies list... that may help give you some info about what sort of vacancies exist in the area.
It can take a long time to become registered... many months, sometimes 3, sometimes longer. So would you give up your job before becoming registered as a childminder?
Are you in England? If so, another list you can use is the one held by Ofsted, which will list all childcare providers within a mileage radius of a postcode. It may well give the same listing as your council website, or it may give a different figure. Whilst 60 may sound a lot, it may be a town location, or part of a city. If there were 60 in the village in which I work, about 1 in 3 households would be a childminder!
Look around your local area, do you see childminders advertising quite a lot - that may be a sign that they are not full, though some childminders may have permanent adverts at some locations.
It can be a struggle in some areas to find children to mind, whilst in other areas it can be hard to find childcare.