I had trouble with my DD when she started solids, too. I found the best thing was to use a little bit of ground flax seed in whatever I was giving her. The unfortunate thing about starting solids is that their little bodies don't always handle it really well.
I found that just that little fiber worked wonders. This was a tip from another mom that had trouble with her daughters also.
A warm bath can also help to soften the stool while still in the belly. This helped later with my little one. I've just learned to add some fiber or fresh veggies and fruit to every day.
Also, you might want to research if some veggies or fruits are more constipating. Like bananas are constipating, so I always try to have her eat some yogurt with ground flaxseed or something else that will help it. I stay away from giving her cheese and bananas in the same day. Those kinds of things. I don't know about avocado.