Welcome to AFF
@pb2034 !
Firstly, Singapore Airlines and Qatar Airways are different ecosystems BUT Velocity/Virgin is the common denominator. So if you want to have the flexibility to use your points to redeem flights on both Singapore and Qatar, you should allocate your points to Velocity.
There are positives and negatives to crediting your paid flights on Qatar to either Velocity or Qatar Privilege Club.
If you allocate your flights to Qatar, the two benefits are, first, that your Qatar status can be used not only on Qatar but also on both Virgin and Qantas (and other Oneworld airlines). Second, reward flights are made available to Qatar Privilege Club members almost a month earlier than to Velocity members (and they're cheaper too, in terms of both points and money). So if your primary aim is to redeem reward flights on Qatar, that's a strong argument for crediting your paid flights to Qatar.
On the other hand allocating your flights to Velocity may have some advantages for you too. You should have just enough points to qualify for Velocity Platinum status, which gives you some cool benefits on Virgin such as "Fly Ahead", free internet and extra-legroom seat selection. Also, you say that you already have "lots of" points with Velocity, so it might be helpful that you keep building up your Velocity stash (which could also come in useful for either redeeming directly on Singapore Airlines, or for converting to KrisFlyer points).
I'm not sure what you mean by "my credit card points probably have to go to VA". If you absolutely positively can't convert any of your credit card points to Qatar Privilege Club, then you may find that sticking to Velocity is your best option. Just be aware that Privilege Club members get first dibs on Qatar reward seats.
One final thing to keep in mind: if you want to redeem points for business class flights for 5 people, you're going to find that almost impossible using either Velocity or Qatar points. Your best bet is to convert your Velocity points to KrisFlyer and book 12 months ahead.