It really depends on how you plan to level. At this stage it wouldn't be apparent, but what follows will make a significant difference to your strategy.

DoH is primarily leveled through Leves. You craft the designated product and hand it in for experience points and gil, plus some other reward. Handing in an HQ (High Quality) product doubles your experience and gil earned. But to produce HQ products, you'll need to (1) keep your gear updated; and (2) sometimes use HQ materials from gathering; and (3) use certain key cross-class skills to push the quality up.

If you go this route, then the usual recommendation is:

1. Level all DoH to 15 for things like Hasty Touch (CUL), Careful Synthesis (WVR) etc
2. Level Cullinarian to Lv.37 for Steady Hand II
3. Level Carpenter to Lv.50 for Byregot's Blessing
4. Level Weaver to Lv.50 for Careful Synthesis II
5. The rest of the crafting jobs to 50

BUT this is only if you plan to be pushing for HQ all the time (well ignore HQ in the first 15 levels as it's not really worth the trouble).

If you don't plan on pushing HQ, then you're looking at doing about 40-60% more Leve hand-ins for all your jobs, but then you would really only need Careful Synthesis from Weaver and keep your main and off-hand tools updated, just churn out the NQ (Normal Quality) products ignoring quality.

This strategy means you just level whatever you want whenever you want, but it will burn through your Leve allowances extremely quickly. You'll be looking at about 18-20 hand-ins per 5 levels. With 4 Leve allowances per 12 hours, that's very slow leveling. Good enough for casually doing it over a few months, but extremely frustrating if you're looking to level your crafters quickly.

My recommendation is to always push for HQ, you'll end up leveling faster and actually understand the interactions between the skills, making it trivial for you to produce the HQ stuff that really matters at level 50.

Oh and a word on leveling DoL: start doing the grand company hand-ins after reaching level 20 or so (gatherers level quickly anyway before 20). They reset every day and provide a huge chunk of experience. By level 35, these grand company hand-ins for gatherers became my main source of experience, giving me like 10% of a level per hand-in for NQ, 20% for HQ, sometimes they even give a star bonus that double the reward, letting me earn 40% of a level for handing in 10 of the required HQ items.