Dear Deepa,
Ofcourse, Day care school / creche is available in Luxembourg ... It is there in every place ... Wherever your location, you will definitely find a creche ... There is not much age restriction mostly from 2 years or 3 years ... but it depends according to creche location ... Hours will also be flexible like 1 or 2 hours, or half or full day ... Fee is always expensive ... that's all I could say ... anyway, you can check as soon as you come to luxembourg, in your nearby location ...