Well, if it's just a junior prom then no, I would not spend too much. Leave the spending for senior prom (though do still enforce a budget). I never went to my junior prom...actually, I don't think they had one at my school. I do have a relative that attended junior prom, and she just wore a semi-formal dress, the kind you'd wear to dinner, so nothing fancy. It was something she already had in her closet, a church dress, actually. Perhaps you can find a dress that she could wear again for a formal event, like a NYE party, or a cruise ship dinner. I would not recommend renting a dress, only because you're stuck with whatever you get. I don't know about your daughter, but ever since I hit puberty, I have never been able to find a dress that fit me well -- ever. I am also 5'1", which means every dress will drag past my feet, and that is the least of my issues. Having a bust makes shopping for a dress impossible, unless it is heavily tailored. Obviously, a rental gown cannot be altered, or else it may not fit the next person that wants to rent it, so then she will end up stuck with an ill-fitting dress and will be upset, if other girls have flattering dresses.
What I would do, is check craigslist (lots of former bridesmaids sell their dresses for less than $100, and prom gowns are an easy find), thrift stores, and the department stores like JC Penney's, Bloomingdale's, or Macy's. Here are many dresses that are $100 or less: https://www.macys.com/shop/junior-clothing/prom-dresses/P... ...although it seems you will have to do a LOT of weeding. I am not sure what Macy's is thinking in advertising such revealing gowns when pretty much every school out there has some degree of a dress code. Yikes, I had no idea that prom dresses had gotten so trashy, sorry. You might be better off choosing a dress from the women's section or the petite section, to avoid such skimpy gowns. I bought my senior prom dress at Bloomingdale's, and I think it cost me about $200. It was on sale and after having tried on over 30 gowns, my mom was happy to have found something I liked and that fit me well, so she just went for it. Of course, some alterations were involved, but nothing too major. Back then, Jessica McClintock stores were the rage and I wanted to look like one of those princesses in a gown, but none of their dresses fit my bust, so this dress was reminiscent of the Jessica McClintock princess gowns, but cheaper.
Amazon.com has some cute gowns that are ridiculously cheap, and with Prime membership, you get free returns. Here are some examples: https://www.amazon.com/Womens-Double-Sheer-Sleeveless-Sil... or https://www.amazon.com/B013WBBSQS-Backless-Bridesmaid-Eve... or https://www.amazon.com/Kayamiya-Womens-Beaded-Flapper-Cha... or https://www.amazon.com/Angerella-Womens-Floral-Vintage-Br... I shopped a vintage 50s dress on Amazon.com and I was actually surprised by how well it fit. I only had to have it hemmed. In my many years of trying on dresses, this was the first time I did not need to have it taken in at the waist or hip area. Good luck, I'm sure she'll look great in whatever gown you choose, and most importantly, remind her to stay safe and have fun!