Question

Especially if I’m using GitHub?
If not, should I (or perhaps someone else) work on such a tool?

Answer 1

add a script that dumps the sql file someplace specific to your project (but inside the project directory).

mysqldump -uroot -p my_db > my_project/my_db.sql

it is juts text so git will pick that file up as changed just like any other. so then just

git add my_db.sql
git commit -m "the schema changed"
git push my_project github master

you may consider the following:

• putting your dump file on github or adding it to the repo means any data there is available for anyone to see, like passwords and usernames so obviously, use fake data.
• you may want to look at the mysqldump options to only dump the schema and not the data http://dev.mysql.com/doc/refman/5.1/en/mysqldump.html