My immediate thoughts:
Don't bother training at this stage. Get some voluntary work with children - in a school, children's centre, playgroup etc. If you can get experience of children with SEN or disabilities, all the better. I don't know where you are, but where I am (London) none of the teaching assistants I have ever known have trained pre-entry to the job. All training has been provided once they got a foot in the door. You have a massive advantage in applying for TA jobs if you have got previous experience of working with children, especially children with additional needs, so if I were you, getting that experience would be my goal. Approach the school your child will be going to first, or other local schools, and ask if you can help out once a week or even month. Reading help is a popular, voluntary foot-in-the-door in many schools. Or if you have a skill that you could offer to contribute - say helping out at a sports club or crafts club or whatever?
TA jobs are highly competitive, especially at primary level. That shouldn't put you off but if I were you, I would scout about on your local authority website and download the job description and person spec for a few TA jobs. What are the asking for? How can you meet their criteria, and where are the gaps in your skills and experience that you can fill?
Bear in mind the following:
TA work is incredibly lowly paid. Most schools don't recruit HLTAs, as they cant afford it. They recruit Level 1 or 2 TAs at a lower rate, ad if you stay with the school for a few years and they come to value you highly, they might up your pay scale or give you higher level training (although TA training has been cut massively in my area because of the economic climate).
Not all TA jobs are just school hours. When I was a TA, I worked 8.15-4.15. I couldn't do the school run in the morning (my kids went to a different school), and my kids were in after school club until 5pm every day.
There are great upsides, though, obviously. If you are thinking about a teaching career, there is really no better way to sound it out than to do a stint of 12 mths or so as a TA. The school holidays are great, too. I got so used to the rhythm of having a holiday every 6 weeks that going back to working outside of a school is a shocker! 
Good luck.