travel to US on H4 then use the stamped H1 to find a job

I hold a valid H1 visa from my employer. Can I travel on H4 visa since my husband is in US then use the stamped H1 visa to look for a job and get H1 transfer if the current employer doesn’t find an opening for me in US.

Yes you can do that but in that case once you are in US on H4, your employer would need to file H4-H1 change od status(COS) before you could start working.