If she is fully-flighted and you're planning on having the garage-door open, and she isn't going to be on a harness/lead/leash, then the answer is a resounding "NO" before you even get to the question of fumes/safety in the garage...I know you said that you're "sure" she'll stay on her stand and not fly away, but those are the famous last words for so many parrot owners that it should be a no-brainer that you should NEVER take a flighted bird outside without them being on a harness and lead of some kind (and I'm sure you know that even birds with their wings clipped can typically take-off and fly for miles just by gliding with the wind, this also happens all the time)...But if she is flighted and you're taking her outside freely with you, you need to stop, regardless of how bonded she is to you, that never matters...There are many, many, many Free-Flight trained birds that have taken-off and never come back, and that's after years of Free-Flight and Recall Training...So if the garage door is going to be open to outside and the bird is going to be free and not on some type of harness/leash, then that makes it a NO right off the bat...period. No exceptions, as this NEVER ends well.
As far as having any bird/parrot in your garage with you, the answer to that is going to depend on each individual garage. I have a workshop in my garage where I restore and repair guitars, and yes, I have several PVC bird stands in the garage and I bring my birds out with me all the time...However: #1) They are ALWAYS wearing their Aviator Harnesses with extension-leads that are securely attached to large, metal hooks I have firmly drilled and attached into the studs in the back wall of my garage. So they are not going anywhere even if they want to, #2) I only take them in the garage/shop with me during warm weather because I always have the garage door open at all times, even though I'm not using any types of chemicals or anything inside of the garage, I still want fresh air for them and for me at all times, so in the cold weather, even though I have propane heaters, the birds don't come out with me, and #3) My garage hasn't EVER been used to house a vehicle, no gas, no chemicals at all, nothing inside the garage/shop as far as fumes....I converted it to a workshop in 2011-2012, and I don't house any types of chemicals, oil, and when I'm using the propane heaters the birds are not there...
The only stuff that i use that is fume-emitting are a few cleaners, polishes, and lemon oil, and they are not in the garage when I'm going to be using anything like this, not ever. And I make sure that if I need to use something like "Goo-Gone" to remove adhesive backing or something like that, they aren't with me, and even so I still use it outside and not inside the garage...If there is any question about what I'll be using on a certain day then they don't come out with me...
Keep in-mind though that my garage is actually built under my house and is actually a part of the walk-out level of my house, so it's not really a typical garage. But the bottom-line is that this has to be looked at on a case-by-case basis, and if there is any question at all then the answer is NO...And again, if your bird can fly and the garage door is open, then she needs to either be on a harness and leash, or not out there in the first place, because all it takes is something falling over and the noise scaring her,
or a barking dog, etc., and she's gone, out the open garage door and you'll never see her again...Just ask Mark about the sound of a falling-ladder and how it's what caused him to lose Maggie, who was free-flight trained