Sounds like nursing to me. I got into nursing after I found out the hard way that law enforcement does not transfer from state to state. Nursing licenses, however, require only a fee to have a license accepted in another state. If your current state happens to be part of the "Compact Nursing License Agreement," then it automatically applies to all other 23 states that are within the compact (although they will still pursue license fees for prolonged assignments).
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As an LPN, you will actually have higher travel nursing marketability than an RN would. First, because LPNs cannot have specialties (per se) and tend to rate less than RN as far as pay. In order to justify paying the higher amounts for an RN (although a travel LPN makes as much or more than a regular RN), travel agencies typically require that RNs have a specialty background (ER, recent Med-surg, L&D). Unfortunately, since the nursing market is inundated with more nurses than hospitals are willing to take, this generally means that some states have as many as 80% of RNs trapped in long-term care (nursing homes) for years.
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Nonetheless, it meets all of your requirements. You can get LPN (diploma) in only 1 year, and can then shoot for RN (associate degree) after another year. There is no need for BSN, although most hospitals are pushing.