Like PP says, every baby is different.
I tried to do some freelance when DS was aboit 5 months. I just couldn't do it, it was a nightmare! It was very stressful and frustrating being unable to do it.
I'm not sure why I thought I could do it, having a baby was so time-consuming that managing to drink a cup of tea while still remotely warm was a challenge I rarely succeeded in!
Imagine trying to work when you're exhausted (haven't had a proper night sleep in MONTHS) constantly interrupted and feel pulled in lots of directions at once. Would you do your best work?
I had to give up trying to work and accept that people get childcare while they work for a reason!
You may not "settle into a routine" that lets you work at home without someine else to look after the baby for a long-time.
The books that give you the idea that you can choose a routine and train your baby into it uf you just try hard enough are lying!
The truth is that some babies take well to a routine and many others just don't. But all of them are totally dependant on you for everything. Trying to force your baby into a mould they don't fit because a book sold you the idea it should be possible is a soul destroying even PND-inducing experience and one worth avoiding!
Much better for everyone IME to go with the flow, e.g. if they want to be near you all the time, get a sling so your baby can nap next to you and you can still get on with life (and actually leave the house!) rather than spending hours shush-patting a baby because the clock and a (non-evidence based) book has told you it's time for them to sleep but the baby really doesn't want to.
People (and baby books) give unreasonable and unattainable ideas about sleeping through too. Many babies don't sleep through for months (or sometimes years). This is NORMAL and largely out of your control.
For some people studying with a baby would be possible.
For many, not at all!
To get a better idea of what it's like with a new baby, Google fourth trimester and I can recommend a book called "What mothers do (especially when it looks like nothing)".
I'm not saying don't study! I am saying you have no idea if it'll be possible until you've met your baby and got an idea of what your new life is like.
What do you want to study? How old would the baby be when you'd start? Would you lose money if you didn't keep to deadline?