A quick page about childcare legislation in Ireland.
Some details of changes from Sept 2014
Can not find a great deal about nannies in Ireland. There is this PDF about taxation in 2012 which may be helpful.
If you look at ads on Gumtree in England/Wales/Scotland then you will see ads from people looking for in home help where some of them may not be aware of employment law and tax law requirements. So in that respect Gumtree (and other advertising sites) I feel are likely to be the same, they are just advert sites they are not advising parents in how to correctly employ a member of staff.
WorkplaceRelations.ie seems to be the place to get information about employment rights including national minimum wage. It seems to me that Workplace Relations Customer Services (Lo-call 1890 80 80 90) would be a place to contact with regard to establishing what employment rights you have, given the recruitment process.
As the parents paid you an amount they decided, not an amount you billed them for, then my guess would be that they would be considered to be your employer. However employment status is not as simple as that, certainly not in England, so I expect the same may be the case in Ireland - there will be various factors taken into account when determining employment status.
Do you communicate with the parents via email at all? It may not be any better than a note but it has the advantage of having a permanent copy of the correspondence.
If you were to ask them for more money, ask them to provide payslips showing tax deductions, would they do so? Or would they terminate the job and find someone who is happy to be paid at a low rate cash in hand?
Consider the implications on your future... if you are not paying towards things like Social Insurance then when you are age 66 (or whatever retirement age it will be come that time in your life as governments do tend to move the retirement age) then you may not have enough Social Insurance Contributions to qualify for the full pension. There are different classes of PRSI, not sure which a nanny would fall under, possibly Class A as that mentions working in "service type employment".
I do not know Irish employment law, so the above is just from what Google tells me. However I hope it at least gives you a starting point in trying to get these parents to do things correctly, rather than paying cash in hand.