My rabbit is about the same age as yours is, and as the others have mentioned, generally, young rabbits get unlimited pellets. However, like Elliriyanna, I’m a little looser about this, as I try to make sure that hay is still the main staple in his diet. He gets about 1/2 cup each day. I’m not sure how big your shot glasses are. Do you have a measuring cup? If so, maybe you could figure out about how many cups he’s getting.
According to the House Rabbit Society, adult rabbits should be getting about a 1/2 cup of pellets per 6 lbs. I’m not sure what kind of rabbit you have, but I believe that smaller rabbits tend to stop growing before bigger ones, so I plan to put my Holland Lop on an adult diet when he’s about six months old. I’m not knowledgeable about other sized rabbits, though.
As far as vegetables go, my rabbit loves romaine and other types of leafy lettuce, as well as dandelion greens. He also eats carrot tops, swiss chard, baby spinach, parsley, dill, and was just introduced to fennel. Of these vegetables, I highly recommend lettuce, since it’s less expensive and the easiest to find. Just avoid iceberg. I buy a pre-washed, undressed spring mix, which is great. The one problem is that the mix also includes chard and baby spinach, so I have to be vigilant about what I’m feeding him, so that he doesn’t get too many vegetables with oxalic acid in each salad.
Adult rabbits get about a cup of vegetables per two pounds. I’m still in the process of putting my rabbit on the adult portion, so he receives about a cup now.
I constantly check the HRS article on vegetables. Binky Bunny also has a great article: https://binkybunny.com/BUNNYINFO/Veg…fault.aspx.