Looking for an apartment that will accept dogs

On immoweb and once you have found an apartment, you have to agree with the landlord to accept the dogs and that is likely to mean a clause in the contract saying you will accept damages the dogs will make. There is no other place to look other than immo websites, agents, shop windows, nothing specific for dogs.

Great - thank you.
I'll keep looking then!

I think you would find it easier if you looked for houses or ground floor apartments, plus perhaps consider going further out of the EU quarter where there is more outdoor space. Try say Auderghem along metro line 5 where you might find a house for less than the cost of an apartment in a trendy part of Ixelles. If you do limit yourself to apartments only, it might be the "syndicat" which owns the building which does not allow dogs in the building, rather than the landlord forbidding it. With houses, the owner of the building is the owner of the house, so there's only one person to negotiate with.