Baby weight in lower percentile, 4 months, starting solids advice

My baby's birth weight was 7lb, 13 oz (3kg, full term 42 weeks) and at 4months its 11lb (4kg). She is in the lower 10% percentile of weight. My paed advised to start solids. I asked whether I can wait till 5.5 months, she said its fine, but not to wait too long. The reason for waiting was because my baby does not have complete head / neck control yet, so was thinking of waiting a while. Though the paed did recommend I get a high-chair with a reclining position for feeding.

Is this weight considered really low? I am wondering whether I should start cereal now, or should I wait a month longer.... a little confused. I was planning to go again for weight check at 5 month and then decide.

Any thoughts appreciated.

thanks,
Cooks.