Congratulations qwimjim! My short answer is I agree with gunthur. You're going to want to have a comfortable base camp from which to choose from a variety of day hikes. Keep in mind you're probably going to be carrying the baby in a front sling/wrap/snugli rather than a backpack carrier because of the hip spread and relative floppy factor. Yes, backpacking is a little crazy if you want my opinion. It's doable for some, but you won't know for yourselves until the time comes.
My advice is to avoid making plans that can't easily be modified. By four months, we were just starting to feel like we had our feet underneath us as new parents. Maybe you'll find it easier than we did. Maybe your baby will eat well and sleep well and be happy during the day. Some are like that, I've heard.
If it was summer right now, I'd be keen to start hiking with the 6 month-old. Life is finding its new normal. We are both back in shape, better rested, and kind of have the logistics figured out. He is big enough, strong enough, and enjoys the backpack carrier. I would feel comfortable trying a short backpack trip. I couldn't say any of those things a couple months ago, but it could be different for you.
I hope you can pull off the Rockies trip. I'm not trying to give you the impression that it's impossible, just that there are a lot of things that will have to fall in your favour, so keep your expectations in check and enjoy the journey!