Ime (but I only have 2 dds!) neither of mine have drunk much in the day. My 13 month old has a long b/f first thing. She then has sips of water during the day (probably 100-150ml in total) then about 200ml of cows' milk at bedtime.
Don't forget that lots of weaning foods (depending on what approach you use) are very "wet" e.g. yoghurts and cereals. I reckon dd has at least 100ml of milk on cereal for example. Even if you do blw, there is a liquid in fruit, veg etc.
Let her "play" with the cup to get her used to it. Also I only use a basic Tommee Tippee cup. Cups with valves can be v difficult for a young child to get any water out of.
She plays a lot with the beaker but seems to prefer, and drinks more, from an open cup.
I'm glad it isn't anything major to worry about. Will she just start to drink more as she needs it?
DD doesn't really have weaning foods now. She got bored of them very quickly and now eats pretty much what I eat, albeit in pieces she can hold. She does have porridge in the morning though and I guess that has maybe 150mls of milk (she eats HUGE portions).
From memory my dd1 (4.8 now) didn't drink a lot until she was about 2. I did worry prior to that but she had plenty of wet nappies etc and no signs of dehydration.
She didn't much like water though so in the end I gave her very diluted juice. She also wasn't keen on milk (other than breast milk but she self weaned at 1 year)
Thankfully my dd2 does like water.
I expect your dd will gradually increase her intake as she needs it. Tbh with my dd2 I kind of think well if she has been guzzling breast milk from 5.30am onwards (for sometimes an hour) and then has a big bowl of porridge, she isn't likely to be really thirsty.
On very hot days (well we only had one or two) I did notice that she tended to pick her cup up more.