Congratulations on your pregnancy!
An early positive test actually was one of my first signs that I was having twins. There definitely is a possible link between an early positive and a multiple pregnancy. Pregnancy tests check for the HCG hormone, and there is generally twice as much HCG when you have twins.
The average singleton pregnancy would have an HCG of 68 on cd 14 (14 days post-conception, the day the period would be expected). HCG levels double just about every 36 hours in healthy pregnancies. Pregnancy tests vary by brand in regards to how much HCG needs to be present in the pee in order for the test to notice it. I *think* the "early response" tests pick up levels of HCG as low as 25. Regular tests usually pick up levels of 50, some cheaper brands don't pick it up until it gets to 100. It should say somewhere on the box how much HCG needs to be present in order for the test to come up positive.
I first tested positive at 9 dpo (and I was quite sure of my dates since I had used an OPT and been artificially inseminated). The test said that it would not be positive until 11 dpo. I was also already feeling a bit of nausea at that point, and just had a feeling that there was more than one baby inside. I called the office where I had done the insemination, and they said that they could do a pregnancy blood test and find out exactly how much HCG I had in me. So, on cd 14 I went in, and my level came back as 405. As I said before, the average for single pregnancies at cd 14 is 68, so I had more than 5 times as much hormone as that. The doctor said that the blood test alone did not mean I was having more than one baby, but gave me a 90% likelihood of multiple pregnancy. From that point on, I was SURE I was having twins, and worried that I might be having triplets until the u/s at 6 weeks.
So, if I were you I would get the blood test, and ask to know the HCG level. It's not 100% accurate (only u/s is), but it can be an indicator.
HTH!
And congrats!