If the $ you are considering spending is extra above and beyond needs for regular expenses *and* savings... I would probably give it a try. If it's stretching in some way, I'd ask myself these questions:
Through a strange series of events that were not planned for and never even considered...dd auditioned on the fly for a voice teacher
It sounds like this wasn't something you'd planned on doing (the audition) - and it's GREAT that your dd auditioned and was accepted - but I'd question how something that wasn't in the plan suddenly moved up to the status of being something worth sacrificing something else for.
Second thing, I think your dd is still relatively young (maybe 7/8?) - I can say without a doubt, no questions about it - the extracurriculars I thought might matter to my kids later on in life changed quite a bit just between 7 and 10 - so I wouldn't want to be putting significant $ into this unless I could look at it as $ spent for now and with no expectation of future benefits from it. Maybe it *will* be something that she carries a benefit from in terms of connections etc for years to come - but don't pay for it if you're going to be surprised if in 2-3 years she decides she wants to quit.
That said, it sounds like a wonderful opportunity. We do pay for enrichment activities for our kids, probably more than I had expected we'd ever pay before I actually had kids

I think the activities add quite a bit to their lives even if they ultimately choose not to continue them. I do think that it's important to have balance and perspective though - rather than being caught up in getting so excited over the prospect of developing talent that you lose perspective over a decision like this. I see a bit of a phenomenon in the early elementary years in extracurricular activities that's very similar to the thing that I saw at school in K/1 - as their kids started school, it seemed that 9 out of every 10 parents I knew thought their child was intellectually gifted and needed extra enrichment at school. When the gifted programs started in 3rd, and when kids actually had gifted testing, all that talk and worry over extra enrichment and "my kid needs so much more" sorta evaporated because statistically speaking... there was no way all those kids could have been in the 95+ percentile of ability

Same thing seems to happen in the activities my kids have participated in that are group-type lessons (dance, gymnastics) - there are tons of younger kids taking part with their parents gushing over how talented their child is. 2-3 years into the sport, so many kids have dropped out because it was more about their parents hoping for prodigies than about what the kids wanted to do or enjoy. So we've tried to stick to keeping our kids in lessons/etc that were things they had fun with, and not worry to much about return on investment

Good luck making your decision!
polarbear