"dream profession" is correct and usable in written English.
You can use it to refer to a profession or career that someone has aspired to for a long time, for example "Her dream profession is to be a firefighter."
When asked about her dream profession, she smiles shyly before admitting she wants to be an air stewardess.
Duncan and Ream began to design a relatively conventional game, in the mold of Joe Danger — another humorous take on a childhood dream profession.
Later, he learned that she had wanted to become a stenographer, and that she, too, was training for her dream profession.
It has long been clear that Ronnie O'Sullivan does not regard snooker as his dream profession – "Really, I don't think it is for me", the five-time world champion said in 2013.
From those early crayon sketches on the skirting board to the more refined — but still frowned upon —— scribblings on school desks to fully-realised comic books — this has always been my dream profession.
It may not have been my choice to miss a wedding or a funeral, but my dream profession was also a black hole; once you're in its gravitational pull, everyone around you must respect that you are indeed trapped in paradise.
While proud of her parents' fame and talents, Fanny was ambivalent about the acting profession, dreaming instead of becoming a writer.
We allowed our children to follow their dreams in whatever profession they set their mind to".
It's called "the actor's dream" (some in the profession use the shorthand "The A. D").
Is it a part of her new profession of dream-realisation and wish-fulfilment - or one of her own dreams?
When I lined up in Beijing I was positive that my competitors had been training to beat me and that if I didn't succeed my dreams of my new profession would be dashed.
