That's a tough question to answer without knowing the horse. IMO I think it's pushing it a little. Generally I find that retraining a horse to a new discipline is a heck of a lot easier (and faster) then breaking a horse and getting them competitive in that discipline. Sounds like you're using dressage to put a proper foundation on her, and that will help out immensely. I took in a really easy going athletic horse that was broke to western pleasure, reining, and driving and had him comfortably jumping 18 in courses within a month. (That's the fastest I've ever taught a horse to jump and prob will be for a while) I waited another few months before raising the fences to about 2"3.
Some of it will depend on how much that horse enjoys jumping. The ones that are a little tenetive take longer. I have a horse that I've been teaching to jump for about 2 or 3 months and he's still trotting crossbars lines. He didn't even want to trot a pole, so this is progress!
Does your horse have a lead change? Some horses take a long long time to get to the point wehr they can comfortably (and accurately) get their changes on course. And every hunter NEEDS one!
Personally, I think you're biggest hindrance is the fact that you have zero jumping experience. (sorry, just stating my opinion!) I don't know how competitive your Arab sporthorse shows are but my kids who just started jumping this summer will *maybe* be going to their first shows this fall at 18 in. And they're on school masters who are teaching them the ropes. If you're really wanting to do this I think the fastest way is for you to learn off a trained horse, and have someone else train the horse to jump until you're both a little more experienced.