Concur that this is too strong. The first- and next-turn effects are both (substantially) better than Merchant Ship's corresponding effects. Additionally, the first-turn effect is better than Wharf's, which is already a power card.
But on principle, yeah, I don't see any philosophical reason why you can't mix +Cards and +$. I agree with popsofctown that such cards get more out of money decks than engine decks. And I can appreciate the argument that all one or the other forces players to commit to a strategy instead of trying to hedge his bets. But I also don't see that as a huge problem if that's specifically what you're going for, or if you're interested in feeding a sort of hybrid engine/money deck, which sometimes happens. That bias is muted in a Duration card, too, where the next-turn draw is non-terminal.
But I think the only way to mix these bonuses in the way you want is this:
Harbor
$5 - Action
Now and at the start of your next turn: +1 Card, +$1.
Following the by-no-means-always-applicable Dominion math of vanilla bonuses (non-terminal +Cards > +$ > terminal +Cards), this is a card whose first-turn effect is weaker than Merchant Ship but whose next-turn effect is stronger than Merchant Ship's. Wharf is a little muddier to compare: it's stronger than Harbor on the second turn, for sure. It's also probably slightly stronger on the first turn, though that's a much closer match. But Dominion math breaks down a little with Wharf, as it's so unusually strong for its cost tier. Bottom line, I don't see any grievous problems with this variation of your idea.