Teething

So all of these sleepless nights have finally been explained - Tali is getting her first tooth.  She's got all of the teething symptoms: gnawing on her hands, swollen gums, teething diaper rash, occasional diarrhea, general uncomfortableness, etc. The only thing she doesn't have is excessive drool. While most babies get their front teeth first, Tali is bucking the trend and getting a tooth a bit farther back in her mouth on the lower right side. I think it's her I-tooth but I'm not sure yet. 

I find it a bit weird that babies get their teeth so early. "Solid" foods aren't introduced until six months and when they are, everything is soft and mushy. They don't start actually chewing foods until somewhere between seven and nine months. So why the need for teeth at four months? I get that it takes time for all of them to grow in but is it really necessary to start so early? It'd be nice if they didn't start coming in until a bit later so that I could have a few weeks of sleep before the sleepless nights resume. As of now, she's only slept through the night when she's gotten shots. She was just getting to the point where she was starting to sleep for a six hour stretch and then the teething began. Can't an overwhelmed new mom catch a break every once in a while? Please?