You should have no problem swapping it for a two bulb fixture.

dont forget to turn the breaker off, not just the switch in the room. and good luck!

Depending on the age of the wiring and the type of fixture chosen you may have issues with the temperature rating of the insulation.
Mnay close mount ceiling fixtures now require 90C conductors.

brickeye, can you explain further? I don't really understand what you mean. The new fixture did indeed have a tag saying it required a 90C conductor, but I don't know what 90 or C or conductor refer to.

Also, which insulation are you referring to? The ceiling mount came with insulation attached to the top. Or do you mean insulation in my attic?

Please help! Thanks.

The 90C is the temperature rating (in degrees cenitgrade) of the insulation on the wires feeding the fixture.
If you look at the conductors in the box and see insulation on the wires that appears about 1/16 inch thick it is likely PVC and only rated 60C.
This type of insulation was standard in NM and AC cable for many years.
If the wiring is less than about 8 years ld it may be 90C rated.

If you have access to the attic and lower rated wiring you can add a junction box near the existing ceiling box.
Move the old cable to the new box, then use new NM to connect to the old ceiling box.
Now you have 90C conductors.

Sorry, brickeye, a couple more questions.

How can I tell whether it's 60C? You mentioned the 60C wire is about 1/16" thick -- what's the thickness of 90C? Knowing the difference will give me more confidence in my measurement.

Also, what's NM?

Thanks for all your help!

Nm is commonly called Romex (Romex is actually a brand name and they make more then just NM).
It is a plastic jacketed cable assembly.

The insulation on the wire is about 1/16 inch thick. The wire is about 3/16 diameter for #14 (two layers of insulation and a #14 conductor).
The 90C insulation is about 1/32 inch thick, so a 90C insulated wire is not even 1/8 inch in diameter (insulation and conductor) for #14.
#12 wire has the same insulation thickness by th econductor is thicker. About 1/10 inch diameter.
If the corctui has a 15 amp fuse or breaker it is most likely #14 and you can use #14 for any extension required.
If you just need a few feet of cable the big box stores sell by the foot.get a 2 foot section of 14-2 NM cable.
It will have two conductors PLUS a bare ground wire (grounds are not counted in cable).

"If the corctui"

Pretty sure this is Circuit

HTH
Chris