My first girl was 5 wks early, weighing 4lb 13oz.
We started her on solids (watery farex cereal) at around 4 1/2 months (on peads advice) because she had reflux. If you bub doesn't have obvious digestive problems you could likely wait til she's about 6mnths before starting solids.
Apart from the reflux she was a happy healthy baby, just very small for her age and it took until she was around 3 to catch up in that area. She was a little slower to walk & talk but again, she's nearly 4 now and you'd never know. That 5 weeks stopped making a difference ages ago.
I'm glad yours is a healthy bub so go with your instinct in regards to solids etc. When she starts showing interest in your food and is wanting extra feeds is the time to start her on watery consistency farex and mashed vegies etc, but introduce just one food at a time, in tiny amounts and slowly build up the quantity and in a few days give her something else to try. Avoid peanut butter, eggs and allergy risk foods until she's closer to a year old.
Sorry to ramble but I hope this helps.
It's hard when different doctors give contradicting advice, problem is babies don't come with a textbook so alot will be up to your own intuition as you know your baby better than anyone else.
Dizie, 2 girls, 2002 & 2003