I did it in Lunar Lakes for my DecaDynasty. I had the Performance Park, Flying V's and Mick's Master Karaoke so I reckon you could do it with those three. The issue with not having the park is that you'll have to wait until level 3 to get gigs, but as in theory you could max the singing career with just playing for tips I don't think that'll be too much of a problem. Gigs do provide a bigger boost to the career but with those three venues you'll be able to get gigs from level 3 and play for tips and do sing-a-grams the rest of the time.
Get the performance-related LTRs and give her the Natural Born Performer trait and you'll be fine, I think.
Lol at Port-A-Potty though.