There are MANY benefits to nursing past age one. In fact, most cultures all around the world practice child-led weaning. Here are some references you give your family:
The World Health Organization recommends that babies be breastfed THROUGH THE SECOND YEAR (ie until age 2). The American Academy of Family Physicians recommends the same thing. Even the American Academy of Pediatrics recommends that babies be breastfed "at least 1 year" - and as long as mom and baby both want to. As another poster said, it's not like your milk magically becomes useless when your baby turns 12 months old. Plus, when you abruptly wean you can have problems with engorgement and mastitis - not an issue when your child gradually decreases what she eats.
There are many health benefits - both physical and psychological - to extended nursing. It still has the same benefits for your baby's immune system even when she's a toddler. Plus, nursing is also about NURTURE - it's a special thing that only YOU get to do with her - it's wonderful bonding and suggle time. MANY moms that I know who weaned their child right at 12 months told me, when they saw me nursing my toddler, that they really had WANTED to nurse for longer but that they stopped because they felt pressured to do so.
Here's the other thing: it's hard for your family at this point to imagine nursing an older child because what they see NOW is you nursing your baby 8x/day. But your child will cut back substantially as she grows. I still nurse my 18-month old son 1-2 times per day - basically morning and night only. I quit pumping at work when he turned one and that made things MUCH easier. But if you're at home this is even simpler. It doesn't get in the way. We don't really need to do it in public anymore (not that I had a problem with that, but now he's old enough that I can say "we'll have good milk when we get home" and that's ok with him). My point is, this is not the obtrusive, all-consuming thing that it is for you right now.
And there is STILL no substitute for comfort like nursing - it's the magic trick that can fix ANYTHING. Believe me - when you're in a hotel room with your husband and daughter (or staying at your in-laws) and it's 2 AM and your daughter is having trouble sleeping in a strange place, EVERYONE will be glad that you can give her the magic boob and she'll go to sleep.
In short, stick to your guns on this one and nurse her as long as you want to. I occasionally get pressure from my husband to quit at this point, and my goal is to wean my son by March, but that's only because we're expecting another baby in June and I don't want him to feel like his milk has been usurped by the new baby.