I guess this isn't strictly a solo-travel experience, but close since it was just me and my little guy.
I recently took my four month old baby with me to Barbados. We drove two hours to the States and took a jetBlue flight from Burlington to JFK, then switched planes to get to Barbados. Once landed, it's an hour's drive to my house in the north of Barbados. So it comes to about ten hours of transit time in total.
It was slightly more complicated on the way back because jetBlue made us change terminals at JFK and transfer my luggage myself, so that made me feel like I walked ten miles, along with taking the monorail and numerous elevators. Anyways, enough about those details. Here are my tips!
I should have remembered my own advice and halved the amount of clothing I brought for him. After all, we were able to do laundry there. I'm an expert packer for myself, but it seems when it comes to son, no luxury was spared. My luggage was overweight both ways, even though I left stuff behind (clothes that no longer fit were donated to victims of the earthquake in Haiti, along with the unused diapers).
Before leaving, I'd read many a message board about travel with young ones and there was a divide over whether to bring two carry-on bags (one for me and one diaper bag for baby) or not. I ended up bringing two and don't regret it. One was our regular diaper bag with the regular essentials and a few added items. The other was both our changes of clothes (we changed from winter clothes into summer stuff before landing in sunny Barbados). I stowed the one with the extra clothes in the overhead and kept the regular diaper one at my feet. I only carried that one to the bathroom for diaper changes and didn't fuss with two bags.
Of course, that brings me to my next point, which was carrying my baby. With jetBlue, I was able to gate check both a stroller and car seat, but did not get them back right outside the plane (unlike Air Canada - all airlines are different). I carried him to and from the plane in an Ergobaby carrier and by then he was usually asleep, so I just plopped my carry-on bags into the stroller and pushed it. When he was awake, I was still able to fit him in the stroller along with my bags, so I didn't have an issue with carrying bags, which was the argument many had for only taking one with them. It's not much fun to carry bags AND a baby. And in light of new rules, it looks like it may be getting harder to carry ANYTHING on board!
Your individual needs are most important, but my opinion is don't be shy to take advantage of whatever the airline you're flying with has to offer - if they allow a separate piece of luggage for the baby, by all means, use it!
When traveling alone with my baby by both plane and train, I found train and plane employees to be exceptionally accommodating and helpful. Listen to their tips and let them take your baby when you need to use the bathroom - they are trained in CPR if anything goes wrong and it's better than asking a complete stranger.
As with any time I use public transit, it's really touch and go if I get any help from strangers. Sometimes I'm surprised how people can watch a mother struggle with a stroller trying to get through a door or up stairs, but in general, there are more good people than bad.
When it comes to your baby crying, so be it. I make no apologies. Babies cry and parents do whatever they can to try and stop it, but babies have little minds of their own, so everyone just has to deal. It was most horrible for my baby when we were on the runway (or in a bus, car or train) and not moving. Once the vehicle starts moving, he's fine, but while waiting on the runway, he had a good long scream. Yes, I got looks from other passengers and I look right back with the same look they give me. If the seatbelt light is on and I cannot stand up to walk around and soothe him, unfortunately he will wail. C'est la vie. Looking at me will not help.
My last bit of advice is to arrive early (I missed a train being late, thinking I could run as fast with a baby as without) and take your time. If you start to get stressed, so will baby. Give yourself plenty of time to get around and try to plan your day while sticking as much to your baby's schedule as possible.
Happy travels and feel free to comment with more tips or questions!