Unless your state has a special provision about getting FMLA-like leave earlier into your job (one state I know has something that kicks in 6 mos in), and unless your contract explicitly states that you can take this sort of time off at this point in your time with your employer, do NOT assume that you can just wait until a few months beforehand and then drop this bomb on them and have a job to come back to.
You need to talk to them NOW and be willing to work with them, because as I see it you have little protection on paper so far.
The hope is that this is a large enough group, and they like you well enough, and it was a bother to find someone they liked as well as you, that they will tough it out without you and keep your job waiting for you to come back to. There is no guarantee, so your best bet is to talk with them, do not come across as entitled in any way, and express the desire to try to make this as less inconvenient as you can for them as far as when you schedule. If you can tough it out a few weeks or what have you to make this easier on them, DO SO. Because in that case they are bending over for you, because you haven't been there long enough to have "earned" the right to certain protections.
There's more to this. If this is related to workman's comp, it's a condition that was made worse at work, you might have recourse. If this is an ADA issue, that can change things, however remember if you invoke ADA, it still might not protect you if the group is small and makes the argument they cannot give you the time off hold onto your job as something they can reasonably accommodate.
You can always contact an attorney with your contract and run your HR dealings by them to try to obtain the best outcome. Keep in mind, I am NOT telling you to let your employer know in any way shape or form that you are getting help from an attorney, it's just one way to be sure you're as protected as you can be in this case (and I don't think so far that you're very protected at all. So don't antagonize your employer. If they don't legally have to give you the time off and keep your job, and they let you do so, it is purely because they are cutting you a break. In that case, act like it.)
Good luck with your new job and your health.