Flying alone with a 13 months old

When I flew with mine at that age. I had him in the stroller and then the largest rucksack I could get in the cabin with al the essentials. Leave yourself loads of time to get through the airport. You need the stress of having to rush. I found staff and other passengers so helpful. Definitely ask for help if you need some one to put your stroller down/ chuck a back in the overhead etc.
when I have done a long haul at night I have tried to keep baby awake in the airport then when up in the air I’ve locally done the night time routine with him. Got him in his pjs, story, milk and he has slept pretty much the entire way. He woke when they turned the lights on for breakfast. I take busy books, reusable stickers and fidget toys. A new book and plenty of snacks. Mine for some reason will not eat plane food so maybe take breakfast with you just in case. We always take a pillow for him to sleep on across me and his seat.

I’ve personally never had an issue pushing the stroller and a small wheelie suitcase, you just push one and pull the other.

Baby’s stuff in their own cabin bag, it’s medically exempt of weight and liquid limits so take what you want and just declare it’s the baby’s at security. They’ll just take a swab and that’s it.

Put him in his pjs to fly, let him walk around the terminal and tire out first. I’ve done long haul night flights alone and most times they’ve slept most of the way 10/12 hours.

I sometimes just reclined by seat and laid her on me but if an empty seat was there I made a blanket bed and let her lay out. Air crew are your best friend, they will help you if you ask. I had crew hold her in the galley and entertain her whilst I used the loo, bring me my meal after others as I was napped trapped, bring me things as I can’t move.