I remember this debate from when the lawmaker Christine Loh went to America so she and her boyfriend could have a surrogate child. According to an article at that time, "IVF is permitted only for infertile married heterosexual couples."
I think this law is vastly unfair. What about people like you? Or gay couples? Or long-term monogamous couples who don't want a legal / church ceremony? Or single women who would make wonderful mothers?
When we went through IVF, they checked over and over to ensure we were married. We had to submit marriage certificates to both the doctor's clinic and the hospital. My husband either had to donate sperm in person, or bring it in in person. One day, he had a very busy day and asked if he could run off to work and I could bring it in for him, and the doctor said no.
I wish you luck. But unless the law has changed, you may have to go to another country to get this done.