Should I buy a seperate dac?

Save your money.

For a first time DAC, I would recommend one above 2K. Any less, one will always want something better up the line, eventually.

Ultimately, yes.

i'd also bet you'd get a significant improvement with the schiit. for less $$ the smsl raw dac 1 is fantastic.

Thank you gdhprentice.  I now have loaded my system into my profile

I had a NAD CD player from around 2010 that cost about $500 at the time. Years later I added a Cambridge dac magic that I bought used for about $300 and it was a more natural sound. My system at the time was JBL speakers , Carver amp, and a Parasound pre. 
In the 90’s I had a Yamaha cd player (1985). When it crapped out I bought another Yamaha (1990). All bottom end players. 
back then, digital was digital right? Well, as soon as I turned it on, I noticed a huge difference. It wasn’t until years later that I learned about better DACs.