No non stops
Emirates is a good choice but as mentioned you have other options
Singapore airlines - one stop in Singapore or Emirates - one stop in Dubai. Stops are usually no longer than 2 hours, the departure/arrival times are great and if you get a good rate total flights are between 22-25 hours with stopover included. Try to avoid China Airlines, rates are cheaper but it's better to pay $200 for a comfortable seat, good service and good food in such a long flight. Korean airlines are cheap and they do a 12h stopover in Seoul where you can apply for a free hotel night and visit the city. However, the flight ends up being really long if your ultimate goal is arriving in Barcelona asap.
In fact I was about to suggest Singapore Airlines ( as is my favorite airline) but I noticed that it now seems to be only a few flights per week , DEmirates have many flights from Sydney to Dubai and they have twice daily Dubai to Barcelona
re China Airlines - I don't think they fly the route TPE to BCN nothing came up
Thank you, that’s very helpful