OK, have a little limited experience of this in a professional capacity but I'm not offering a substitute for RL professional advice (just want to make that clear, sorry). I also had depression as a teenager, though I've never used cannabis, so can empathise a bit with your dd.
Practically there is stuff you can do to help her get over this but it is complicated as the drug addiction and depression both need to be addressed. I think she probably could do with RL professional help and someone outside of the home to talk to confidentially about how she feels - but it could be harder to convince her it would help, and if you push too hard you risk alienating her further.
However, I thinks it's good that you're trying to address the issues - my parents knew I was depressed but ignored it, they thought it was one of those things you just 'get over' - it's not, your daughter may take a while to get better but the fact you're there for her will be very important in her recovery.
Spend time with her away from the house on your own if possible. The reason I think this is important is that she associates home with being in her room and smoking and therefore feeling low. Taking her out of the situation will help break the habit and the mood associated with it. You said you had another child - try and make arrangements for them to have time with someone else (don't know if you have DP/DH). You'll need to make sures/he doesn't feel left out though and make time for him/her too.
Find an activity which is fun that you can do together REGULARLY (eg art class, swimming, cycling etc) - this will give you a time each week she can look forward too and feel positive about and she'll know that she will have your attention too.
Get her to help you in the home/going shopping if you don't already, she might not like it at first but it's harder to smoke a spliff if you're doing something and receiving praise from you will give her a boost.
In answer to your first point in the opening post - my professional experience was while working as a therapist on an in-patient unit. I would strongly recommend you try and get her to seek help now to avoid ending up as an inpatient. Not all cannabis users end up there, and your daughter would be unlikely to, but it saddened me a lot to see young people having had psychotic breakdowns or having become suicidal. There's much debate over whether cannabis causes these things or whether it's used by people who already have the problems but it's generally agreed that it doesn't help a situation.
I think it's also important though to try and put it into perspective, if this is just a 'blip' - if this is recent and your daughter is generally a happy girl and something has happened to make her feel like this, do give her some time to get over it before going overboard. However, if this behaviour has been ongoing then I fully understand your concern and the urgency you feel is necessary in sorting it out.
Sorry for the long post, hope it's been of some help.