Yes, you can earn United Airlines Premier Qualifying Points (PQP) and Premier Qualifying Flights (PQF) when booking through Routespring and billing to your company, provided that your MileagePlus number is included in the reservation. United's MileagePlus program allows members to accrue PQP and PQF on flights operated by United and its partner airlines, regardless of the booking channel. Ensure that your MileagePlus number is correctly added to your booking to receive the appropriate credits.

Here's an help article on United Airline's website: How to Earn Premier Status?