A lot of fairly judgey comments on this thread.
I want to outline that it's important that your partner genuinely wants kids with you in the near future if you do do this. You both need to be enthusiastic and willing, but...
OP being on a minimum wage doesn't matter if her husband is supportive and earning enough money to cover them both. They could be living in a less expensive area where 30k is fine. Childcare is expensive so she'll likely be cutting her hours down anyway. A lot of minimum wage jobs offer flexibility that regular, better paid employment, doesn't. It also gives OP time to figure out a career path if the job she is currently in isn't a long-term goal for her.
Being 23 is a perfectly acceptable time to have children. OP, you can have a family 'early', and once they're off to school, work on your career then. You won't need to take breaks out for children in your 30s and you can race up the employment ladder if you work hard. You'll also have the added motivation of wanting to give your kids the best start in life when money begins to matter. You'll also have more years when you're older to travel child-free, and probably be better off money wise than you would be now. Just something to consider.
We don't have to follow the stereotypical path society lays down for us. Follow the path you want to. At the end of the day, you'll be the one carrying children and giving birth, if you'd rather do it when you're younger than older, that's absolutely your call to make.
Your partner seems a bit wishy-washy on what he wants, though. You obviously do want to progress the relationship, but he seems to keep putting barriers up. Doesn't want to get engaged until in a higher paying role (yet is in one and still nothing). Doesn't want kids until you're in your 30s (so years away). Doesn't want kids before marriage (but won't propose currently). You need to establish what is a genuine barrier and what is BS to hold you off. A lot of men put barriers in front of committal acts because they don't want to commit, but also don't want to lose someone they're having sex and fun times with. I'm not saying that's your partner, but you need to ensure he's serious about your future.
OP, it's the 21st century. Women are allowed to want things, and if it turns out your partner simply doesn't want what you do, there's no shame in leaving. Similarly, maybe a serious conversation is all that's needed to give things a kick-start.
Good luck. I hope everything is figured out, and hopefully, you can start trying for a baby soon if the circumstances are right.