Yes. I did. A couple of weeks ago. It is very easy. You go do Ikea Dubai, you shop and after you pay (of course you tell the casher before invoicing) you go to the Delivery Service and ask them to ship the goods to Doha. Ikea has an agreement with ARAMEX. It took only 3-4 days for my goods to be home delivered in Doha. The Aramex person in charge of it in Doha is a very professional and efficient guy. I contacted him before going to Dubai to shop at Ikea, so he knew about it and he contacted his collegues in Dubai and he personally kept in touch with me till the goods were delivered.
Pricewise, things are a little bit different. It was not really cheap.
You have a minimum charge, plus a cost per kilo or volumetric weight whichever is higher, plus custom taxes, plus document legalization costs, plus the cost of goods packaging in pallets etc. It is a little bit coplicated to eplain in a few words, but
if you would like, please contact me. I would me more than happy to show you all the exact costs and give you the name and number of the Aramex person I dealed with.
I am new in Doha, so it would be really a pleasure to offer you a coffee while giving you all infos!!! And share the problems we have to deal with being new here!