As far as pet care, I have done this a lot! In 1st grade I got a puppy and my family had him until he was 18 years old and I was out of college! Then I got a cat and my family has had her so far for about 10! I have also pet sat/house sat for like 20 years. :)
As far as childcare, I have been a babysitter / nanny for ages and I work at a school. I also have a baby myself. We can discuss whether he would generally be coming with me or staying home.
I do have my own transportation.