Ask an Immigration Solicitor. Get an Answer ASAP.
Some children born between 2000 and 2006 in the UK to EEA nationals will be British automatically but given that your child was born in 2010 your child will not be entitled. Given that you have been in the UK for 10 years and presumably you have worked all this time when you apply for permanent residence and you are granted, your child will be entitled to be registered as a British citizen. Do this make sense? If not please ask.