I have feels about this. Good lordy, I have feels.
One, is that we need, need, need to avoid stereotypical, "barefoot, pregnant, and in the kitchen" attitudes among our men and dwarves. That is not to say that they need to be gender equal, just that it needs to be handled in a more nuanced way. I'm thinking, especially with the dwarves, that any unhealthy social norms be of the "benevolent sexism" sort. And if you're not familiar with that term no, it's not a good thing.
A lot of Hobbit fanfic is terrible (but of what genre is that not true), but one thing the good ones tend to be really good at is considering the consequences of a "male-dominated but female-dependent society". That is -- dwarf women are one in three, and Tolkien says many choose not to marry. So you will always have more males than females, especially more unmarried males, and what does that mean for your culture? Tolkien's Word of God indicates that dwarf females at least have the right, first to choose whether or not they wish to marry, and second whom. Beyond that, I think it's in keeping with canon to depict females as sheltered: either by being kept at home or being presented as males to outsiders.
The major struggle a female dwarf is likely to feel isn't that she's considered weak/silly/incapable -- I see no reason we can't depict them as well-educated, trained craftsmen just like their brothers -- but that they're too precious. The dwarfling girl who wants to be a warrior won't be told female's aren't strong enough to fight, but that the society can't risk it. Dwarf women can't be forced to wed, but do many of them, especially perhaps in noble families, feel a pressure to do so in order for family/blood lines to continue?
If women are so few, and "breeders" (to be blunt) are fewer, than a lot of archaic human attitudes we're familiar with won't apply. A dalliance before marriage, for example, probably won't ruin a girl's prospects -- it's not as if her suitors have a plethora of other options, after all. A female -- any female -- might have to fight tooth and nail not to be stuck on a pedestal, worshiped and adored from afar.
All this is to (for me, briefly?) say that dwarf gender issues are there, but they're going to be very different from our average experience.
There is something to the idea of Dwarf females being "too important" to waste in combat. There is pretty good precedent to that in human cultures. Obviously there are the considerations of the average physical attributes involved, but early human civilizations would realize quite quickly that males are quite expendable in comparison to females. It may have actually given rise to polygamy, as males would have a far lower life expectancy.
The "male-dominated but female-dependent society" has a lot of precedent. Think about cultures that have a "bride price" vs. a "dowery". Of course, there sexist implications of both, but it is an interesting distinction nonetheless.