I used to do it when I was younger, pay rate usually depends on how many catalogues you have to deliver (so usually close to Xmas is good pay lol).
It is often quite time consuming, as you can have quite a lot of homes, I had a couple hundred - possibly more! I can't remember. And for each house you needed to have all the catalogues put together already, that process usually took a few hours in itself. BUT - that's done at home, so not necessarily all bad in your situation?
As for the delivering, imo thats the easiest part, I used a pram (one where "baby" would face me) and loaded it up with the catalogues so I didn't have to make so many trips back to the car. Which perhaps you could use a carrier for bub and use the pram like that? That's if you did it when they were with you.
Most weeks it seemed relatively worth it, but others you only get like 2-3 catalogues and maybe upto $100. But it's also less work, ya know?
You also generally have a deadline as you need to get the catalogues out before the sales actually start, so once you start delivering, I try to get it all done at once so it's over asap, as you can get into trouble.
It could be all different now, but I doubt it would, that'd mean more work for the suppliers, etc. lol HTH!