My opinion...
Ideally she must not be going out of the country when her H4 extn is pending..
but cancelling a trip is too troublesome, so just make sure that once she comes back, try to apply for a new visa at st louis for revalidation 60 days before her H4 visa expiry.
I dont know if the fellows in st louis will tally that the I-94 numbers match for the H4 approval notice and the airport I-94..but you can take a chance.
otherwise she may have to take another trip to activate the H4 I-94 so that she does not fall out of status.
Some attorneys will say that for H4 extns travel may not matter so much. ask your lawyer about his opinion.
If she is in India and then you get her H4 approval here..send her the original and she can get a new H4 stamp and then come back ...that is ok too.