M.O.
I think feeding the baby at 4 months really depends on the baby him/herself. My son was so ready to eat at four months. The books all said that the first feeding will be difficult, you'll be lucky to get a good spoonful into him, etc.. Please, he ate the whole bowl the first time and by five months was onto a bunch of different fruits and veggies. But I understand that some babies really aren't interested, so I think you have to take your cue from that.
As for digestion, I don't think babies digest things fully and you will see that in his poo. Carrots will still look pretty much like carrots. But my boy (8 months now) has been thriving and loves food - all different kinds.
I should also mention that we also started him at 4 months on food because he was drinking so much milk. I breastfeed him, but since I pump I knew that he was getting about 30 oz of milk a day, which was a lot of food and energy for me to produce.
All that to say, personally I found it fun to introduce my LO to food, he loves it and he's still getting lots of breastmilk.