I empathize with your need to afk suddenly at unexpected times to attend to your children. When you're in the thick of things, you can't beat feign death (monk, necro, sk) for safety when you need to check on a baby.
Shaman can certainly solo well through all stages of development, with a gradual progression from Tanking in Teh Face [sic] at the lower levels, to primarily root-rotting at higher levels (64+). The reason for this is twofold: (1) at lower levels, all our dots have an initial damage component that tends to break root (making it more annoying to root/rot versus tanking) whereas our dots 64+ do not; and (2) lower level mobs don't hit as hard as higher level mobs, relative to your hitpoints at the time (tanking becomes less viable at higher levels, although doable in a pinch).
It used to be that soloing for melee classes was drastically cut down in efficiency around 60+. I'm not sure how the new out-of-combat regen is going to affect the soloability of monks and sks, but obviously it's going to help them.
Shaman are definitely desirable in a group at all levels.
I'm not sure how LGuk would be for a shaman. You can make IVU pots to help get around the dungeon. Runners would be a pain (as they will always be for a shaman), and pulling more than one caster could rapidly get painful. It's a great zone - I soloed a lot here with my paladin and necro, but I could pacify pull singles. I think there are probably better options for a shaman.
Your primary mode of killing would be pulling with slow, then dotting the mob while you melee anemically and your puppy adds his dps. Our wolf pets have much fewer hitpoints than magician or necro pets of the same level, and aren't generally suited to off-tanking. They do make acceptable speedbumps if a pull goes wrong and you need to train the zone.
If you can get your hands on a jaundiced bone bracer, your soloing will improve 46-55ish.