I know that your situation may not be exactly like mine was, but as mothers we all face similar struggles. I finished a very rigorous Practical Nursing program all the while juggling 3 kids (ages at the time were 10, 7, and 2 1/2 yo), and a husband who worked full time, so to answer your question it is certainly "do-able" it just takes a LOT of organization and prioritizing.
The one great thing about the position you are in with regards to having a 9 month old is that you don't have to feel guilty about missing any school or sports functions while you are at clinicals or studying. To maximize your time at home with your baby, make sure that you get in as much study time as you can while on campus, I always packed a lunch and stayed on campus to study intead of leaving with the crowd at lunch time to eat. I also found that it helped to record lectures and listen to them on the ride back and forth to school. Study during your little one's nap time and of course a little bit after he/she goes to bed for the night. There are going to be somedays where no matter how much planning out time for studying you do, that little one is just gonna need his mama and you are gonna have to just push the books aside for a little bit and cuddle him/her. If possible get the grandparents on board and have them help as much as possible so that you can have extra study time and/or be able to relax and have a brief moment to yourself. I also paid a trustworthy teenager to comeover somedays, even while I was home, to tend to the kids while I was in my room studying. That allowed me to study for a bit with out worrying about the kids burning the house down, yet also be able to get up and take a breather from the studying and emerge from my room to spend a few minutes with the kids before going back for more so to speak.
I am scheduled to start the RN program this Fall and will once again face this same struggle only this time I have 4 kids (15,12,8, and 2) and a husband to deal with, so we will see if I can follow my own advice once again. I wish you the best of luck on your journey to becoming an RN, don't let the negative voices get you down, if you can dream it you can achieve it!!