Could this be rewritten as

その赤ん坊は歩くが出来る。

No

その赤ん坊は歩くことが出来る。

And I'm wonding what the purpose of こと is.

The "koto" nominalizes the verb. You can't directly have a verb in front of ga (at least I can't think of any examples where you would). Generally, you are going to need either "koto" or "no".

I just googled it and found this:
http://www.timwerx.net/language/jpverbs/lesson31.htm

Paludis wrote:

Hi, I recently joined this website and I'm currently working my way through RtK1. I'm also starting to do the AJATT sentences thing. I was looking at this sentence

その赤ん坊は歩くことが出来る。

And I'm wonding what the purpose of こと is.

Could this be rewritten as

その赤ん坊は歩くが出来る。

and still mean the same thing?

I don't know if a native would understand that sentence. He/she may even not realize something is grammatically wrong - specially in the context of a conversation if you talk fast. Anyway, that would be grammatically incorrect.

howdycowdy pointed out a grammatically correct option. You could also just use the potential form of the verb and the meaning would be the same. I.e.: その赤ん坊は歩ける。

Also can anyone recommend a good forum for asking this kind of question? I have a feeling I'll have a lot of them and I don't want to bother you guys all the time, seeing as this site seems to be mainly about kanji learning.

Thanks!

Check Jgram . Sometimes some examples aren't the best, but in my opinion the site can be pretty useful, specially the comments.

Basically, the meaning is the same, but ことができる is a bit more formal.

It's good to know, because it allows you to have more variety in your speaking/writing (instead of always using the same one), and again, is a bit more formal.

When in doubt, longer == more formal is a safe bet.

And if you don't already own the Dictionary of Basic Japanese Grammar and the Dictionary of Intermediate Japanese Grammar, I *HIGHLY* suggest you pick them up.  Well worth the investment, and a great deal more reliable and well written than j-gram.