It depends actually, if customers will trust your site enough to be convinced that you are indeed selling authentic products and if you are able to find a reliable suppliers for the designer names you want to sell.
It is legal so long as you source your products through an authorized distributor/reseller who can readily provide you with a documents to prove the authenticity of their products.
Designer products are relatively hard to source through dropshipping so it is a bit of a challenge in finding reliable suppliers with authentic designer products.
Yes customs can intercept your product anytime especially if they are counterfeit or copies.
All the best!