Mine are a little older than yours at 2.5 and nearly 4, but I remember 1 was a hard age. Not a baby, but not a toddler.
I find that getting out the house every morning and just pottering in the afternoons works well for us. Also finding a morning activity that they can both do is a bonus. Playgroups are pretty good for that - different toys, older one can crash around, baby can potter, and there's always tea and biscuits. I don't care much for the adult social aspect, although I've met some nice people, but it's good entertainment for the kids. Messy play sessions also cater for both age ranges which is good.
So, i get out and do something in the morning - some days all 3 of us, and some days the eldest is at preschool. Home for lunch usually, but sometimes in the park etc. I have a strict 'rest hour' where both children are in their room - the eldest plays, and the youngest sometimes sleeps but sometimes plays. Rest finishes at 2/2.30 depending on how the day is, so there's only a couple of hours until dinner! Lego, park, library, playdoh, drawing, small world, playing cafe, baking (occasionally), in the garden, reading, camping under the table etc. We spend 10minutes putting toys away, and then I let them watch TV for 30minutes while I make dinner.
I try to encourage them to play by themselves because it is good for them. I do a lot of "Well you set the Playmobil people out and I'll be back in 2 minutes after I put the washing away"
When my youngest got a bit older and they started playing together was a huge milestone.