Exact domain names do get ranked well in SEs and are a good choice when relevant like yours. They will get punished if what is on the site does not match the domain, or inbound links seem spammy.
If your site is about Personalized Birthday Gifts, then I see no reason why not to use the domain. I would not use exact anchor text when building manual links as most sites will list your URL as the anchor so that is covered. I would build links like this (presuming you have done your keyword research)
- Birthday Gifts
- Gifts for Birthdays
- Birthday Gift Ideas
- Personalized Gifts
The cons with exact domains is that you are boxed in as many see it. You can not easily sell wedding supplies. This comes into play with GEO TLDs such as using a location in your TLD such as San Diego or California. If you expand out of this area, then you boxed yourself in without great marketing.
Just Cabinets sells furniture, so they have marketed themselves out of selling just cabinets, but you can see the amount of effort it would take.
If you are going to sell nothing but birthday gifts, then I see no reason not to use the exact match TLD.
I hope that answered your question.
