First of all - rest your mommyheart at ease....the amount of milk a baby will get from suckling is vastly different than the amount of milk your body will letdown when pumping. Hormones produced in your brain help the letdown process even more so no fear there.
Also - six months is the MINIMUM age for introducing solids. That means a baby should AT LEAST six months old at the very youngest before giving them solids. But many children still get all their nutrients they need from breastmilk beyond that six month mark. It's not a madical date where they suddenly need to have solids.
If she's not ready she's not ready. Continue nursing her. Try again in another month.
My oldest son was ready for solid food at 6 months 3 weeks - my second born not until well past 7 1/2 months. It varies child to child.
Is she soiling diapers every day? Wets 2 or 3 times a day minimum? A nice poopy one every other day at the least?
Does she have active, alert times throughout the day where she is happy, awake and playful?
Is she growing? Either heavier or taller? (not necessarily both at the same time!)
If yes than DO NOT WORRY. :-)
You are making enough milk for her or she would be one very pissy baby.
ETA - don't worry about her refusing the bottle either. Both my children went straight from breast to sippy cups. They hated artificial nipples. So try the soft, rubber spouted sippy cups (Valves are bad!!) but don't push it.