Been twice with partner (1998 and 1999) but this was BC (before children). Saw some parents with children, even babies, and thought they were very brave/mad! Young ones seemed to have a great time though.
The main problems at Glastonbury for us were the weather, the crowds, and the infamous toilet facilities. In 1998 it rained (and rained and rained...) and trenchfoot became a real problem for many (seriously!). In 1999 it was hot and sunny and sunburn became an issue (nicer problem though). There is very little shade at the site.
Essentials: torch, toilet roll, hand wash gel (you can get a dry type that you do not need to rinse off), plastic bags (to keep things dry and even to keep your feet dry - put over your socks and wear under your boots if the place starts to resemble the Somme), spare socks, waterproofs, and some good waterproof walking boots, sun screen, hats, watch. Don't recall any baby changing facilities. The washing facilities are very rudimentary (maybe 3 cold water taps per field of 1000's of campers) with big queues. There were some showers, but perhaps only for the brave. But maybe things have improved since we went!
BTW when you pitch your tent in the morning the site will probably be quite empty, but when you return later at night you will find the place absolutely full of tents with barely enough space between them to walk. It can take AGES to find your tent in the dark. Try to pitch near a landmark. Many campers put up a flag, drape brighly coloured material over their tent or paint logos on their tents to help them find them again. You have been warned!
I would imagine the main problems of taking a baby will be the amount of kit you will have to carry from the car to the site (can take about 30 minutes), and keeping them fed and clean. I wouldn't take a pushchair: most routes on the site are rough tracks, if it rains this would be hell. Also I think babies would get scared being so low down in the crowds.
Perhaps leave stuff in your car in case you change your mind - you can return to your car at any time. Don't take much food - the on-site food is maninly excellent with loads of stalls selling a variety of grub. Stalls sell bottled water. The site is vast, can take ages to traverse in the crowds.
Keep valuables on you - even at night (we didnt have probs, but some have). Cash required - surprising amount of stuff to buy. (We returned with batiks, pottery, clothes..)
The Kids field would be good to visit, although your baby is too young, I expect there would be lots of families around there. Its also near the circus area, which is good fun. Also not as crowded as other places. Green fields are full of new agey stuff etc and v chilled. The craft field is near there and also v interesting. Only prob is getting there through the crowds. Now they have restricted numbers, I hope this is better. Crowds were my big prob.
Where to camp? Furthest away from entrances is quietest, but obviously you have to carry everthing there. Furthest away from dance tent for good nights sleep. Don't camp in too remote a place, is less secure.
Would love to go again, but decided that if we ever did we wouldn't take kids. Too loud and crowded. Also hard physical work for you? Apparently Guildford fest is best for families (baby changing, showers & creche), but have to put up with dodgy old bands! (its aimed at late 30s, which I might be - but it doesn't mean I want to listen to Madness and Boy George any more!) Folk festis attract families, but you have to like folk music..
Everyone should go to Glastonbury at least once. Is a fantastic experience, even if it rains, line-up looks great this year (sigh) - have a great time! You lucky, lucky...
ps. Do let us know how you get on, we might change our minds next year!