Like Ludy mentioned, a lot of the baby-readying doesn’t have to happen right away because the baby isn’t doing that much for a while. So don’t stress too much.
On the other hand, some of the things we put off I vaguely wish we had done in advance, simply because after the baby comes, you don’t have as much time to devote to projects (or shopping for projects).
The thing I would recommend the most is to put child-proof latch hooks on the floor-level cabinets in the kitchen and bathroom. We first put all the poisonous things in higher up cabinets, which I thought might settle the issue, but then I realized it was really tedious to keep having to tidy up all the harmless things our baby would pull out of the cabinets. I would say this started at around 9 months. I left one cabinet un-childproofed, and keep Tupperware and plastic bowls in it – this keeps her occupied while I am cooking or cleaning in the kitchen, and it’s easy enough to chuck all the Tupperware back in one place.
In addition to the latches, or if you decide not to go that way, it’s a good idea to keep cleaning products, alcohol, and other things you would especially not want a baby to drink on high shelves (especially in terms of the cleaning products, we kept all those under the sink before the baby’s arrival) and use your bottom cabinets for baby-safe things only. Just in CASE the baby gets past the latch, you don’t need her drinking Drano Max. Same thing with items stored on the bottoms/tops of closets.
This is a little specific to our house, but we had to rig up another latch on one of our doors so that it could stay open enough for the cat to go in and out (to get to his litter box) but with a small enough gap that the baby can’t go through.
Oh, cat toys. A lot of our cat toys had small parts that a baby could swallow or choke on, so we put those away and limited the cat to a few basic toys. One of my favorite pictures though is of our baby cheerfully teething on a grotty old catnip toy covered in cat hair and lord knows what else.
Some of our radiators had sections of exposed pipe that get quite hot, so we purchased foam insulators for them.
If you don’t already, I would suggest getting in the habit of keeping a box of Kleenex in each room (like EVERY ROOM) because there are a lot of times with a baby that you could use a Kleenex right the heck now.