I would wait until you have actually lived together before thinking about moving into marriage territory.
If you are seriously loved up etc then there is no rush.
Just enjoy living together for at least six months first. I knew I wanted to marry my partner after a year together, but we both agreed that living together was an important first step. We are engaged now, and obviously I still want to marry him, but now it's less of a "I'M SO HAPPY LET'S GET MARRIED" type affair and more of a "I love this person, we work well, we've done the non glamorous stuff together, so let's get married".
It was him who wanted to wait more than I did, but I am really happy that we didn't rush into anything.
I think the woman proposing works if the guy has made it clear he wants to get married but the woman needed a bit more time to think about it, where two people have been living together for a long time and both have a very relaxed attitude towards the idea of getting married, or when the man is super hyper liberal and doesn't give a shit.
My partner would have been horrified if I had proposed. I think most men see it as their role to do the asking, and their partner doing it would take away what they see as a huge life event for them. Even the most modern, liberal guys I know have said it would make them feel really uncomfortable.
One guy friend described it as:
Imagine you are getting married and you are excited about going wedding dress shopping with your mum and sisters, trying on the dresses, trying on the veils, looking through make up artists portfolios or watching tutorials on pinterest, choosing the perfect shoes...etc. Then your fiancé comes home with a dress and says "hey I got your dress for you and my sister is going to do your make up". Even if the dress is nice and the sister is good at make up, you've seen had those experiences taken away from you, which you grew up understanding were YOUR role, not theirs.
It's obviously not a direct comparison, but I think you should tread carefully. For a lot of men, the actual proposal is the only part of the "getting married" journey that they have sole control over and can surprise the bride with. For everything else, let's face it, the bride might ask for opinions but will generally go for her preference, and will know exactly what is going to happen on the day.