How soon should I expect my child cross over 1000?

The ballpark expectation should be 1 year after s/he gets his/her initial rating, depending on how hard your child can work.

When your child is young, such as under age 10, it's very easy for him/her to improve quickly. S/he has a lot of time to study, solve puzzles, play games, and play in tournaments. S/he can afford to make mistakes here and there, but still maintain progress. Even if your child is older than age 10, s/he should have better comprehension to absorb knowledge quickly.

Most students who have been staying with chess have crossed over 1000 in a year. There are a few who might get their initial rating above 1000. This can be a blessing or curse, because the initial rating is not stable. If they drop down for a few tournaments to their real ratings, then they might be discouraged dramatically and quit. Of course, if they could hold on to it, then they have saved a lot of time.

If your child can't get above 1000 after 2 or 3 years, either s/he is not working hard enough, or s/he is not in it. Not everyone has to play chess, so find another hobby for him/her. It's completely normal.