Reddit mentions of Rhodia Webnotebook - A5 (5.5 x 8.25 inches), Lined, Black

https://www.amazon.com/dp/B002TEADOS/

I use Rhodia Webnotebooks and haven't turned back.

Not *exactly what you're looking for, but I'm very happy with my system. I have a Saddleback Leather notebook cover filled with a Rhodia Webnotebook.

But they do...

You've gotten excellent advice on inks, and some on notebooks. You mentioned being overwhelmed by the choices, but wanting a sturdy notebook that can handle fountain pen ink. There are a few choices mentioned in here, but perhaps I can help summarize this. Key thing you will want is a high gsm (Grams per Square Meter), since a high gsm means thicker paper.

• Red and Black: 96 sheets, standard ruling, 90gsm, casebound, hardcover. Personally, no experience with this, but I've heard there's no bleed through with fountain pens.
  
  
• Seven Seas "WRITER" A5 Journal: 240 sheets, ruling is 7mm, 52 gsm Tomoe River paper, thread-bound for binding, cover is impregnated cloth (but you can buy a leather cover). Also no experience with this either.
  
  
• Leuchtturm1917 Medium Size Hardcover A5 Notebook: 125 sheets, ruling can be either lined/graph/dot grid, 70 gsm, thread-bound, hardcover with some sort of leather covering. I've been using these since 2013, and in my first notebook, my handwriting hasn't changed from the day I had written in it with Diamine Ancient Copper. You would still want sturdier ink than what I had used. The paper is cream colored, and smooth. Bleed through is rare.
  
  
• Rhodia Webnotebook A5: 80 sheets, ruling can be either lined/graph/dot grid, 90 gsm, thread bound, leatherette hard cover. I've always enjoyed Rhodia paper, and while I haven't used this particular product, the paper is much smoother than the Leuchtturm1917, and there's less ghosting. The paper also appears whiter to me than the Leuchtturm1917.
  
  
• Rhodia Goalbook A5: 112 sheets, ruling is dot grid, 90gsm, thread bound, leatherette hard cover. Throwing this in the options list, since you get a few more sheets. Also wanted to point out that the cover appears to be flexible.
  
  
• Scribbles That Matter, Pro: 100 sheets approx, ruling is dot grid, 100gsm, thread bound, vegan leather hard cover. The sheets are smooth, and a bit brighter than the Leuchtturm1917, but a bit more ivory than the Rhodia. Great paper, and the cover feels more durable and pleasant than the L1917. With fountain pens, I have yet to bleed through this paper, and the ghosting (seeing what is written on the other side of the sheet) is very minimal. If I push you towards any notebook, it'll be this one. It also comes with a penloop that is not useless, unlike the L1917.
  
  
• Lemome Thick Classic Notebook with Pen Loop A5: 90 sheets, ruling is either dot grid or lined, 90 sheets, 125 gsm, thread bound, leatherette cover. Just got this the other day, and the pages are thick and smooth so far. No bleed through or ghosting with fountain pen ink yet.
  
  
• Lemome Hardcover A5 with Pen Holder: 92 sheets, ruling is dot grid, 100g, thread bound, leather hardcover. Just an option to put in here, it has a pen loop, and the paper seems to be slightly less thick than the prior Lemome notebook.
  
  Wishing you and your daughter the best during these hard times.

There seems to be good reviews of this TN clone here on Reddit. ZLYC Leather Travelers Notebook - no affiliation. You could then print out your own inserts if you want to go the TN route.

5x8" = A5 size, roughly. Jet Pens has the most comprehensive notebook buying guide. It and Goulet have a notebook search with the "size=A5" filter that would be a great way to see what's out there.

I got my brother a Leuchtturm 1917 and he thinks it's pretty nice. Dot grid with page numbers too. You'll hear a lot of people say it's inferior paper for fountain pens compared to the Rhodia Webnotebook, but it does absorb and dry ink quicker so when you have to close the book and go, the ink doesn't smear onto the opposite page. I personally love my webnotebook but it does take a little while before I'm comfortable flipping onto the next page. The ultimate A5 notebook is the Nanami Seven Seas Writer with 480 pages of Tomoe River paper (the fountain pen holy grail paper), but it always sells out when it comes on sale. I just checked their website and they're restocking "Late May" which could be any time in the next couple of weeks, so keep your eye out!

Edit: didn't see your college budget: Black n Red notebooks are budget- and fountain pen-friendly. They're $6-7 a pop, available in twin-wire or hardcover, so go hog wild.

I remember looking for one a while back, and the only thing I could find was the crappy blue Moleskin that's 3.5" x 5.5".

I ended up ordering a Rhodia Webnotebook from Amazon. They're pretty nice. The pages are a little smooth for my taste but they handle pen and ink pretty well. They've also got a webbed sleeve in the back for holding misc.

The Leuchtturm 1917 is also very popular for dotted notebooks.