One thing to consider as to why bookshelves can fall over, is the damn skirting board. That's why they can't go flush to the wall. I'd recommend getting a stud finder. They don't cost too much and it will come in handy to put up pictures etc, because knocking for thickness can be difficult. You may find wiring or something else that sounds thick.

Maybe go to Bunnings and ask one of the dudes there. Find out what sort or brackets you need and bolts etc. Another thing is, google it. You never know if the step by step diy is on a website somewhere.

Put the heaviest books on the bottom and the lightest things on the top. Perhaps put doors on the shelves, or use some of that pvc coated wire with hooks on the end to attach to eye hooks on the sides of the shelves, strung along the middle of the shelf to prevent books being pulled out easily. The wire is easily unhooked and rehooked when required.

And make sure your DH doesn't go overboard on baby-proofing. You may later dread having to unclip things to go about daily business. But I do think bolting shelves to the wall is a very good thing to do. My DD climbs onto shelves all the time here. Thankfully the shelves are mostly empty. She likes to sit on the bottom shelves like its a big chair. Its so cute!

Good luck!