Q.1 - If my wife doesnt work yet, will UKBA extend my visa ?
A1. It is a new application for a residence card that you make. UKBA will ask for proof the EEA national is exercising treaty rights before issuing a residence card. So, No, not until the EEA proves they are exercising treaty rights.
You could claim EEA is self-sufficient if you have Comprehensive Sickness Insurance for all of you. Even then UKBA could try to argue as your wife has NEVER exercised treaty rights in her own right, then she shouldn't be able to rely on your earnings to qualify as self-sufficient. The reason being, she is supposed to exercise treaty rights FIRST that then gives you the right to work. Not you working so she can exercise treaty rights.
( For the first three months the EEA national is assumed to be exercising treaty rights. After that they need to prove it).
Q.2- How to apply for visa ? is it possible to apply online ?
A2. EEA2 residence card application as family member if you intend to stay in the UK. Postal application only.
Find it here:
http://www.ukba.homeoffice.gov.uk/sitec ... /eea21.pdf
UKBA information is here:
http://www.ukba.homeoffice.gov.uk/eucit ... ts-family/
Q.3- If my baby get benefit, is it will be harmful for my visa ?
A3. Yes. It will probably confirm to UKBA that the EEA national is not exercising treaty rights and is an unreasonable burden and so residence documents should not be issued.
Read the bottom of the discussion from the link where UKBA's stance is explained.
If you asked my opinion, I would advise that you do not apply for a residence card under your present circumstances. Others may advise differently.
Wait until the EEA national is working part-time at least, at the time of your application, so you have proof of EEA exercising treaty rights as a worker.
If the EEA national works, then you will be allowed to claim benefits and this should not affect your EEA2 residence card application.