No minimum length per se, but the more proof that you have of the relationship being "serious" the better. Photos with each other's parents, evidence of holidays together, etc, etc.
And you do have to be legally married.
When applying for my (Filipina) wife's visa it took 10 weeks and several visits by me to Immigration with more documents and evidence. They somewhat quaintly asked for any letters, with postmarks. The best I could do was a printout of a Skype log, which the officer seemed amused by!