Hi Boru38.
There is no issue with taking a contract for Belgium via your Irish Ltd. company. However the problem with doing that is recovering the cost of expenses that you will incur while you there. The Revenue is being very inflexible about this at the moment for contractors.
You could contact your local revenue office, give them the details of the contract etc and there is a possibility they will allow you to claim expenses tax free. If they agree to this, make sure you get it in writing. However a word of caution, this might prompt the revenue to take a closer look at your company.
I am not sure how common umbrella companies are in Belgium, when I was there a few years ago I didn't come across them, but then again I didn't go looking for them either. I am not sure how practical using a Belgian umbrella company would be. Belgian bureaucracy is a bit heavy.
It might be more financially beneficial to you if take a staff position for the duration of the contract if that is a possibility.
It is very hard to take a short term contract abroad as an independent contractor in the current climate. I have done so in the past but wouldn't do it now. What I am looking at currently is setting up overseas either UK or Holland and only take contracts abroad for a few years.