Assuming you sent from the DoubleTree Convention Center to the Drop-Off location on Harbor Blvd, the price would be about $8.50 plus tip according to TaxiFareFinder.com (they get mentioned up on the WDW transportation board).
And to the OP, I can't answer your question exactly, but I called another hotel by the convention center to talk about transportation to DL. They suggested using a taxi instead of ART and said it would be about $7 for a regular, $10 for a mini-van that seats 6. I think there is one company contracted with Disneyland and they have a counter at the drop off on the Harbor side.
When we're staying at the Convention Center hotels (usually Hilton, but we've stayed at the Doubletree too), we just walk across Harbor and take the Toy Story Shuttle. It's free and there's almost always one waiting there.
I took a cab from that hotel to the taxi stop when I went for the 24hr thing and it cost me almost $12 with tip. It's not a long walk, but I was alone and didn't want to walk at 1am myself. As posted, it's across the street from the Toy Story lot which was a very convenient way to get to and from the park.
We are in DL now have used Uber Plus to get to my parents hotel which is about the same distance you want to go and it was $12. Last Oct we stayed at Doubletree and used ART or we would walk to the park.
When we're staying at the Convention Center hotels (usually Hilton, but we've stayed at the Doubletree too), we just walk across Harbor and take the Toy Story Shuttle. It's free and there's almost always one waiting there.
I am glad to know this, we are staying at the new Homewood suites and wanted to use the Toy Story shuttle, I didn't know if the wait times were better than ART or worse
When we're staying at the Convention Center hotels (usually Hilton, but we've stayed at the Doubletree too), we just walk across Harbor and take the Toy Story Shuttle. It's free and there's almost always one waiting there.
I am glad to know this, we are staying at the new Homewood suites and wanted to use the Toy Story shuttle, I didn't know if the wait times were better than ART or worse
You also might want to consider walking. To get to the Toy Story lot you'll be walking away from DL to get there. The distance from the new Homewood to the parks isn't all that bad.