I personally would give it a couple weeks without any wheat (keep an eye out because there is wheat in everything) and then try again and see what happens. Spitting up and a rash are such normal events and could be totally coincidental, and as it wasn't severe, I wouldn't myself feel nervous about trying again. But I would give it some time to make sure if it is illness coming on or teething or a post-viral rash for a virus she had already that you didn't realise, etc., it has a chance to clear out of her system first.
My daughter had a fairly severe reaction to pumpkin seeds (pumpkin seed butter, which is a really random thing, but she loved it) when she was about 7 months old. I actually just thought she had a virus and didn't connect it at all to the food. Basically, it was really severe projectile vomiting about 2 hours after eating (like it went like 3 feet across the room) and she got really listless and groggy after. She'd had the pumpkin seed butter for lunch on toast, but it didn't occur to me to link the two (especially as she'd had it on a few occasions before this without any problem). Then about a month later, we had it again and 2 hours after, same severe projectile vomiting, her whole face broke out in hives, and her eyes got puffy and red, and she was similarly really groggy and out of it (but breathing was fine, which is why I didn't totally panic). We put two and two together and realised the only thing in common with these two occasions is that she'd had the pumpkin seed butter about 2 hours before (and not any other time in between). We saw the GP who advised eliminating it until after a year and trying again. We did that and then tried it again at about 14/15 months and she was fine. Actually, pumpkin seeds are now one of her favourite snacks!
So just based on my own experience, I would try again in a few weeks and see what happens. If you see a similar or more severe response, you might see your doctor about it. Allergy testing isn't very helpful at this age and not always very accurate, so more than likely they'll just tell you to wait and try again later like we did. But I would give it some time on your own first and try again in a few weeks and see what happens.