Tax law is complicated the world over, and as a general rule you should seek the advise of a tax specialist in the jurisdiction where you'll need to pay taxes, they'll also likely be able to incorporate a company for you if that will be the best option.
In 2001 Ireland moved from a system of tax-free allowance, to one based upon tax credits, the principal tax credit being €1,650 (directly offset against your tax bill), which is roughly equivalent to a tax free allowance of €8,250, you can find out more on Wikipedia entry for Taxation in Ireland.
It's also worth pointing out that as in most countries, there are tax benefits to being a registered company:
As a sole trader you pay income tax at the same rates as PAYE employees, but based on your net annual profit (i.e. after the deduction of legitimate expenses). If you’re operating as a limited company, however, you could be paying tax at a mere 12.5 per cent or even at just 10 per cent. This means that there can be a considerable tax advantage in operating a business through a company instead of as an individual.
via Just Landed
Ireland is known for it's low corporate tax rates (EU customers of many multinationals will often be billed by the Irish subsidiary of the company for exactly this reason; e.g. Amazon AWS), so you may find that the turnover at which it makes sense to incorporate is significantly lower than it would be in Germany. Again, you should seek professional advise specific to your situation.
To find an accountant in Ireland you might want to try the Chartered Accountants Ireland website's Member Search, and I'd suggest looking for one in the town or city you'll be living.
