It's quite pretty but it does sound dated now as it was so popular in the late 80s/90s and hasn't really been popular since. I went to school myself with quite a few, who would all be mid/late 30s by now. I've taught one, but right at the start of my career so she'd be around 20 now. A friend has a niece called Jade, but again she's in her early 20s now.
As long as you're ok with her having a name which is more popular with your own generation than her own, there's nothing fundamentally wrong with the choice. It is a nice name, just one which seems to have fallen out of favour. Amber is another gemstone name which seems to be rapidly falling out of favour, despite being quite popular 10-15 years ago.
I'm not so sure Jade will pick up again soon, despite other gem names being in. Opal and Pearl (for example) are names which were popular 3 generations ago, our grandparents generation, and they are the names which generally come back into fashion. Many people having babies now will know of several Jades their own age, therefore won't be as keen to use them.
A similar example is Holly. Both nature and ie/y names are so in right now, so I find it surprising this one continues to fall down the charts each year, rather than rise up again, but I assume it's because (unlike many of the currently popular plant or nature names, and ie/y names) Holly was actually quite popular among our own generation so people are less keen on picking a name which reminds them of people they went to school with.
Sorry, I went off on a tangent there explaining why I don't think Jade will be back in favour any time soon! However, as long as you and her dad love it that's all that matters. It's certainly not unusable and lots of people actively seek a more unusual name, which it probably will be within her own generation.