Waiting to start work as an NP

I graduate in August and I've had several interviews that all require relocating (which I'm fine with) but they haven't been exactly what I want. I want to do child and adolescent psych but most places want me to see adults or see adults and potentially build a child/adolescent caseload. I had one offer from a pediatrician office that also does mental health but they wanted me to sign a contract immediately and only have FNPs on board. I don't feel like it would offer enough support as a new grad. 

I had a fellowship I really wanted ask me to apply next year as I wouldn't be licensed in time to start.

I've been considering travel nursing until I can apply to the fellowship again for next year, but the fellowship of course is not assured. It will not open up for applications until January and individuals are selected in April. 

Would it hurt my chances finding a job later if I start applying again 6-12 months after graduation?

My thoughts were traveling to various peds hospitals for behavioral health would help with networking as well for later job searches.